Maths-
General
Easy

Question

Find the value of 𝑚 & 𝑛 to make a true statement.
(𝑚𝑥 + 𝑛𝑦)2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2

Hint:

The methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2

The correct answer is: (2,2) and (-2,-2).


    (mx + ny)2 can be written as (mx + ny)(mx + ny)
    (mx + ny)(mx + ny) = mx(mx + ny) + ny(mx + ny)
    =  mx(mx) +  mx(ny) + ny(mx) + ny(ny)
    = m2x2 + mnxy + mnxy + n2y2
    = m2x2 + 2mnxy + n2y2
    Now, m2x2 + 2mnxy + n2y2 = 4𝑥2 + 12𝑥𝑦 + 9𝑦2
    Comparing both sides, we get
    m2 = 4, n = 9, 2mn = 12
    So, m = +2 or -2 , n = +3 or -3
    Considering 2mn = 12, there are two combinations possible
    1. m = +2 and n = +2
    2. m = -2 and n = -2
    Final Answer:
    Hence, the values of (m, n) are (2,2) and (-2,-2).

    Related Questions to study

    General
    Maths-

    37. In an academic contest correct answers earn 12 points and incorrect answers lose 5
    points. In the final round, school A starts with 165 points and gives the same number
    of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
    i)Which equation models the scoring in the final round and the outcome of the contest

    Answer:
    • Hint:
    ○    Form equation using the given information.
    ○    Take the variable value as x or any alphabet.
    • Step by step explanation:
    ○    Given:
    correct answer = 12 points
    incorrect answers = -5 points
    School A starts with 165 points and gives the same number of correct and incorrect answers.
    School B starts with 65 points and gives no incorrect answers and the same number of                           correct answers as school A
    ○    Step 1:
    ○    Let the number of correct answers given by school A be x.
    So, the number of incorrect answers is also x.
    At school A starts with 165 points. After giving x correct and a incorrect answers points will be
    rightwards double arrow165 + 12x - 5x

    School B starts with 65 points. Schools are given the same number of correct answers as                       school A and no incorrect answers. So, their points will be
    rightwards double arrow65 + 12x
    ○    Step 2:
    ○    As both schools tied
    ∴ 165 + 12x - 5x = 65 + 12x
    • Final Answer:
    Correct option:
    Option B. 165 + 12x - 5x = 65 + 12x

    37. In an academic contest correct answers earn 12 points and incorrect answers lose 5
    points. In the final round, school A starts with 165 points and gives the same number
    of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
    i)Which equation models the scoring in the final round and the outcome of the contest

    Maths-General
    Answer:
    • Hint:
    ○    Form equation using the given information.
    ○    Take the variable value as x or any alphabet.
    • Step by step explanation:
    ○    Given:
    correct answer = 12 points
    incorrect answers = -5 points
    School A starts with 165 points and gives the same number of correct and incorrect answers.
    School B starts with 65 points and gives no incorrect answers and the same number of                           correct answers as school A
    ○    Step 1:
    ○    Let the number of correct answers given by school A be x.
    So, the number of incorrect answers is also x.
    At school A starts with 165 points. After giving x correct and a incorrect answers points will be
    rightwards double arrow165 + 12x - 5x

    School B starts with 65 points. Schools are given the same number of correct answers as                       school A and no incorrect answers. So, their points will be
    rightwards double arrow65 + 12x
    ○    Step 2:
    ○    As both schools tied
    ∴ 165 + 12x - 5x = 65 + 12x
    • Final Answer:
    Correct option:
    Option B. 165 + 12x - 5x = 65 + 12x
    General
    Maths-

    Find the value of x. Identify the theorem used to find the answer.

    Answer:
    • Hints:
      • Perpendicular bisector theorem
      • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step by step explanation: 
      • Given:
    AB = 2x.
    AC = 4x – 4
    AD is perpendicular bisector at BC.
    • Step 1:
    • In  straight triangle ABC text ,  end text
    AD is perpendicular bisector.
    A is point on AD
    A is equidistant from B and C.
    So,
    AB = AC
    2x = 4x – 4
    4 = 4x – 2x
    4 = 2x
    4 over 2 equals x
    x = 2
    • Final Answer: 
                 Hence, x = 2.
    Perpendicular bisector theorem is used.

    Find the value of x. Identify the theorem used to find the answer.

    Maths-General
    Answer:
    • Hints:
      • Perpendicular bisector theorem
      • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step by step explanation: 
      • Given:
    AB = 2x.
    AC = 4x – 4
    AD is perpendicular bisector at BC.
    • Step 1:
    • In  straight triangle ABC text ,  end text
    AD is perpendicular bisector.
    A is point on AD
    A is equidistant from B and C.
    So,
    AB = AC
    2x = 4x – 4
    4 = 4x – 2x
    4 = 2x
    4 over 2 equals x
    x = 2
    • Final Answer: 
                 Hence, x = 2.
    Perpendicular bisector theorem is used.
    General
    Maths-

    Where is the circumcentre located in any right triangle? Write a coordinate proof of this result.

     

    Answer:
    • Hints:
    • Distance between two points having coordinates (x1, y1) and (x2, y2) is given by formula:
    • Distance =square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root
    • Step by step explanation: 
      • Step 1:
      • Let triangle ABO,
    where,
    O = (0, 0)
    A = (2a, 0)
    B = (0, 2b).
    • Step 1:
    • Let triangle ABO, where:

    The midpoint of BC is given by,
    not stretchy rightwards double arrow fraction numerator 0 plus 2 a over denominator 2 end fraction comma fraction numerator 2 b plus 0 over denominator 2 end fraction
    not stretchy rightwards double arrow left parenthesis a comma b right parenthesis
    So, the perpendicular bisector will intersect BC at M (a, b).
    Equation of line BC is
    y minus y subscript 1 equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction open parentheses x minus x subscript 1 close parentheses
    y minus 0 equals fraction numerator 2 b minus 0 over denominator 0 minus 2 a end fraction left parenthesis x minus 2 a right parenthesis
    y equals fraction numerator 2 b over denominator negative 2 a end fraction left parenthesis x minus 2 a right parenthesis
    y equals fraction numerator negative b over denominator a end fraction left parenthesis x minus 2 a right parenthesis
    And point M (a, b) satisfy above equation
    b equals fraction numerator negative b over denominator a end fraction left parenthesis a minus 2 a right parenthesis
    b equals fraction numerator negative b over denominator a end fraction left parenthesis negative a right parenthesis
    b = b
    Hence, point M (a, b) lies on BC.
    • Final Answer: 
    Hence, circumcentre of right angle triangle lie on midpoint of hypotenuse.

    Where is the circumcentre located in any right triangle? Write a coordinate proof of this result.

     

    Maths-General
    Answer:
    • Hints:
    • Distance between two points having coordinates (x1, y1) and (x2, y2) is given by formula:
    • Distance =square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root
    • Step by step explanation: 
      • Step 1:
      • Let triangle ABO,
    where,
    O = (0, 0)
    A = (2a, 0)
    B = (0, 2b).
    • Step 1:
    • Let triangle ABO, where:

    The midpoint of BC is given by,
    not stretchy rightwards double arrow fraction numerator 0 plus 2 a over denominator 2 end fraction comma fraction numerator 2 b plus 0 over denominator 2 end fraction
    not stretchy rightwards double arrow left parenthesis a comma b right parenthesis
    So, the perpendicular bisector will intersect BC at M (a, b).
    Equation of line BC is
    y minus y subscript 1 equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction open parentheses x minus x subscript 1 close parentheses
    y minus 0 equals fraction numerator 2 b minus 0 over denominator 0 minus 2 a end fraction left parenthesis x minus 2 a right parenthesis
    y equals fraction numerator 2 b over denominator negative 2 a end fraction left parenthesis x minus 2 a right parenthesis
    y equals fraction numerator negative b over denominator a end fraction left parenthesis x minus 2 a right parenthesis
    And point M (a, b) satisfy above equation
    b equals fraction numerator negative b over denominator a end fraction left parenthesis a minus 2 a right parenthesis
    b equals fraction numerator negative b over denominator a end fraction left parenthesis negative a right parenthesis
    b = b
    Hence, point M (a, b) lies on BC.
    • Final Answer: 
    Hence, circumcentre of right angle triangle lie on midpoint of hypotenuse.
    parallel
    General
    Maths-

    Ayush is choosing between two health clubs. Health club 1: Membership R s 22 and
    Monthly fee R s 24.50. Health club 2: Membership R s 47.00 , monthly fee R s 18.25
    . After how many months will the total cost for each health club be the same ?

    Answer:
    • Hint:
    ○    The concept used in the question is of the quadratic equation.
    • Step by step explanation:
    ○    Given:
    Health club 1: Membership R s 22 and Monthly fee R s 24.50
    Health club 2: Membership R s 47.00 , monthly fee R s 18.25.
    ○    Step 1:
    ○    Let the number of months after which the total cost is equal be x.
    So, for Health club 1:
    After x months, total cost will be =
    rightwards double arrowMembership Rs 22 + fee for x months
    rightwards double arrow 22 + 24.50x
    Health club 2:
    After x months, total cost will be =
    rightwards double arrowMembership R s 47 + fee for x months
    rightwards double arrow 47 + 18.25x
    ○    Step 2:
    ○    Equalize both costs to get number of months
    rightwards double arrow22 + 24.50x = 47 + 18.25x
    rightwards double arrow24.50x - 18.25x= 47 - 22
    rightwards double arrow6.25x = 25
    rightwards double arrowx = fraction numerator 25 over denominator 6.25 end fraction
    rightwards double arrowx = 4
    • Final Answer:
    Hence, after 4 months the total cost of each health club will be equal.

    Ayush is choosing between two health clubs. Health club 1: Membership R s 22 and
    Monthly fee R s 24.50. Health club 2: Membership R s 47.00 , monthly fee R s 18.25
    . After how many months will the total cost for each health club be the same ?

    Maths-General
    Answer:
    • Hint:
    ○    The concept used in the question is of the quadratic equation.
    • Step by step explanation:
    ○    Given:
    Health club 1: Membership R s 22 and Monthly fee R s 24.50
    Health club 2: Membership R s 47.00 , monthly fee R s 18.25.
    ○    Step 1:
    ○    Let the number of months after which the total cost is equal be x.
    So, for Health club 1:
    After x months, total cost will be =
    rightwards double arrowMembership Rs 22 + fee for x months
    rightwards double arrow 22 + 24.50x
    Health club 2:
    After x months, total cost will be =
    rightwards double arrowMembership R s 47 + fee for x months
    rightwards double arrow 47 + 18.25x
    ○    Step 2:
    ○    Equalize both costs to get number of months
    rightwards double arrow22 + 24.50x = 47 + 18.25x
    rightwards double arrow24.50x - 18.25x= 47 - 22
    rightwards double arrow6.25x = 25
    rightwards double arrowx = fraction numerator 25 over denominator 6.25 end fraction
    rightwards double arrowx = 4
    • Final Answer:
    Hence, after 4 months the total cost of each health club will be equal.
    General
    Maths-

    Find the gradient and  y- Intercept of the line x plus 2 y equals 14

    Hint:
    Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, compare the equation with the standard form to get the slope and the y-intercept.
    Step by step solution:
    The given equation of the line is
    x + 2y = 14
    We need to convert this equation in the slope-intercept form of the line, which is
    y = mx + c
    Rewriting the given equation, we have
    2y = 14 - x
    Dividing by 2, we get
    y equals 14 over 2 minus x over 2
    Simplifying, we get
    y equals negative 1 half x plus 7
    Comparing the above equation with , we get
    straight m equals negative 1 half semicolon straight c equals 7
    Thus, we get
    Gradient = negative 1 half
    y-intercept = 7
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope = negative a over b  and y-intercept =c over b , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula.

    Find the gradient and  y- Intercept of the line x plus 2 y equals 14

    Maths-General
    Hint:
    Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, compare the equation with the standard form to get the slope and the y-intercept.
    Step by step solution:
    The given equation of the line is
    x + 2y = 14
    We need to convert this equation in the slope-intercept form of the line, which is
    y = mx + c
    Rewriting the given equation, we have
    2y = 14 - x
    Dividing by 2, we get
    y equals 14 over 2 minus x over 2
    Simplifying, we get
    y equals negative 1 half x plus 7
    Comparing the above equation with , we get
    straight m equals negative 1 half semicolon straight c equals 7
    Thus, we get
    Gradient = negative 1 half
    y-intercept = 7
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope = negative a over b  and y-intercept =c over b , where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula.
    General
    Maths-

    We can express any constant  in the variable form without changing its value as

    Explanation:
    • We have given a constant
    • We have to find how we can express any constant 𝑘 in the variable form without changing its value.
    Step 1 of 1:
    We have given a constant k
    We have to find how we can express any constant 𝑘 in the variable form without changing its value
    We know that x0 = 1
    So After multiplying it with any constant, it will not change its value.
    So,kx0 is the answer
    Hence, Option C is correct.

    We can express any constant  in the variable form without changing its value as

    Maths-General
    Explanation:
    • We have given a constant
    • We have to find how we can express any constant 𝑘 in the variable form without changing its value.
    Step 1 of 1:
    We have given a constant k
    We have to find how we can express any constant 𝑘 in the variable form without changing its value
    We know that x0 = 1
    So After multiplying it with any constant, it will not change its value.
    So,kx0 is the answer
    Hence, Option C is correct.
    parallel
    General
    Maths-

    x0 = ?

    x0 = ?

    Maths-General
    General
    Maths-

    State and prove the Perpendicular Bisector Theorem.

    Answer:
    • To prove: 
      • Perpendicular Bisector Theorem:

    • Proof: 
    • Statement:
      • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step 1:
    Let consider given figure,

    Let arbitrary point C on perpendicular bisector.
    In which,
    CD is perpendicular bisector on AB.
    Hence,
    AD = DB
    CD = CD (common)
    straight angle ADC equals straight angle BDC equals 90 to the power of ring operator
    So, according to SAS rule
    straight triangle ACE approximately equal to straight triangle ACE
    Hence,
    CA = CB
    So, any point on perpendicular bisector is at equal distance from end points of line segment.
    Hence proved.

    State and prove the Perpendicular Bisector Theorem.

    Maths-General
    Answer:
    • To prove: 
      • Perpendicular Bisector Theorem:

    • Proof: 
    • Statement:
      • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step 1:
    Let consider given figure,

    Let arbitrary point C on perpendicular bisector.
    In which,
    CD is perpendicular bisector on AB.
    Hence,
    AD = DB
    CD = CD (common)
    straight angle ADC equals straight angle BDC equals 90 to the power of ring operator
    So, according to SAS rule
    straight triangle ACE approximately equal to straight triangle ACE
    Hence,
    CA = CB
    So, any point on perpendicular bisector is at equal distance from end points of line segment.
    Hence proved.
    General
    Maths-

    What is a monomial? Explain with an example.

    Explanation:
    • We have to define monomial by giving an example.
    Step 1 of 1:
    A monomial is an expression with only one term.
    The examples are: 3x, 6y

    What is a monomial? Explain with an example.

    Maths-General
    Explanation:
    • We have to define monomial by giving an example.
    Step 1 of 1:
    A monomial is an expression with only one term.
    The examples are: 3x, 6y
    parallel
    General
    Maths-

    Find the equation of a line that passes through left parenthesis negative 3 comma 1 right parenthesis and left parenthesis 2 comma negative 14 right parenthesis

    Hint:
    We are given two points and we need to find the equation of the line passing through them. The equation of a line passing through two points (a, b) and (c, d) is
    fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction
    Step by step solution:
    Let the given points be denoted by
    (a, b) = (-3, 1)
    (c, d) = (2, -14)
    The equation of a line passing through two points (a, b) and (c, d) is
    fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction
    Using the above points, we have
    fraction numerator y minus left parenthesis negative 14 right parenthesis over denominator negative 14 minus 1 end fraction equals fraction numerator x minus 2 over denominator 2 minus left parenthesis negative 3 right parenthesis end fraction
    Simplifying the above equation, we have
    fraction numerator y plus 14 over denominator negative 15 end fraction equals fraction numerator x minus 2 over denominator 2 plus 3 end fraction
    not stretchy rightwards double arrow fraction numerator y plus 14 over denominator negative 15 end fraction equals fraction numerator x minus 2 over denominator 5 end fraction
    Cross multiplying, we get
    5(y + 14) = -15(x - 2)
    Expanding the factors, we have
    5y + 70 = -15x + 30
    Taking all the terms in the left hand side, we have
    15x + 5y + 70 - 30 = 0
    Finally, the equation of the line is
    15x + 5y + 40 = 0
    Dividing the equation throughout by 5, we get
    3x + y + 8 = 0
    This is the required equation.
    Note:
    We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0,, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.

    Find the equation of a line that passes through left parenthesis negative 3 comma 1 right parenthesis and left parenthesis 2 comma negative 14 right parenthesis

    Maths-General
    Hint:
    We are given two points and we need to find the equation of the line passing through them. The equation of a line passing through two points (a, b) and (c, d) is
    fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction
    Step by step solution:
    Let the given points be denoted by
    (a, b) = (-3, 1)
    (c, d) = (2, -14)
    The equation of a line passing through two points (a, b) and (c, d) is
    fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction
    Using the above points, we have
    fraction numerator y minus left parenthesis negative 14 right parenthesis over denominator negative 14 minus 1 end fraction equals fraction numerator x minus 2 over denominator 2 minus left parenthesis negative 3 right parenthesis end fraction
    Simplifying the above equation, we have
    fraction numerator y plus 14 over denominator negative 15 end fraction equals fraction numerator x minus 2 over denominator 2 plus 3 end fraction
    not stretchy rightwards double arrow fraction numerator y plus 14 over denominator negative 15 end fraction equals fraction numerator x minus 2 over denominator 5 end fraction
    Cross multiplying, we get
    5(y + 14) = -15(x - 2)
    Expanding the factors, we have
    5y + 70 = -15x + 30
    Taking all the terms in the left hand side, we have
    15x + 5y + 70 - 30 = 0
    Finally, the equation of the line is
    15x + 5y + 40 = 0
    Dividing the equation throughout by 5, we get
    3x + y + 8 = 0
    This is the required equation.
    Note:
    We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0,, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.
    General
    Maths-

    The degree of 25x2y23 is

    Explanation:
    • We have been given a polynomial expression in the question for which we have to find its degree.
    Step 1 of 1:
    We have given an expression
    We know that degree is highest power of variable present in polynomial.
    So,
    The degree of is
    Degree of  is
    Degree of is
    So, Total degree is

    Hence, Option B is correct.

    The degree of 25x2y23 is

    Maths-General
    Explanation:
    • We have been given a polynomial expression in the question for which we have to find its degree.
    Step 1 of 1:
    We have given an expression
    We know that degree is highest power of variable present in polynomial.
    So,
    The degree of is
    Degree of  is
    Degree of is
    So, Total degree is

    Hence, Option B is correct.
    General
    Maths-

    Ritu  earns R s 680 in commission and is paid R s 10.25 per hour. Karina earns R s
    410 in commissions and is paid R s 12.50 per hour. What will you find if you solve
    for x in the equation 10.25x + 680 = 12.5x + 480

    Answer:
    • Hint:
    ○   To solve the equation, group terms with the same coefficient on one side and numbers on                      the other side.
    • Step by step explanation:
    ○    Given:
    10.25x + 680 = 12.5x + 480
    ○    Step 1:
    ○    Solve the equation.
    ○    Group the like terms
    10.25x + 680 = 12.5x + 480
    rightwards double arrow680 - 480 = 12.5x - 10.25x
    rightwards double arrow200 = 2.25x
    ○    Step 2:
    ○    Divide both side with 2.25
    not stretchy rightwards double arrow fraction numerator 200 over denominator 2.25 end fraction equals fraction numerator 2.25 x over denominator 2.25 end fraction
    rightwards double arrow88.88 = x
    • Final Answer:
    Hence, the x = 88.88.

    Ritu  earns R s 680 in commission and is paid R s 10.25 per hour. Karina earns R s
    410 in commissions and is paid R s 12.50 per hour. What will you find if you solve
    for x in the equation 10.25x + 680 = 12.5x + 480

    Maths-General
    Answer:
    • Hint:
    ○   To solve the equation, group terms with the same coefficient on one side and numbers on                      the other side.
    • Step by step explanation:
    ○    Given:
    10.25x + 680 = 12.5x + 480
    ○    Step 1:
    ○    Solve the equation.
    ○    Group the like terms
    10.25x + 680 = 12.5x + 480
    rightwards double arrow680 - 480 = 12.5x - 10.25x
    rightwards double arrow200 = 2.25x
    ○    Step 2:
    ○    Divide both side with 2.25
    not stretchy rightwards double arrow fraction numerator 200 over denominator 2.25 end fraction equals fraction numerator 2.25 x over denominator 2.25 end fraction
    rightwards double arrow88.88 = x
    • Final Answer:
    Hence, the x = 88.88.
    parallel
    General
    Maths-

    If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then the triangle is ____ isosceles.

    Answer:
    • Hints:
    • Perpendicular bisector theorem
    • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step by step explanation: 
    • Step 1:
    Let consider given figure,

    Let arbitrary point C on perpendicular bisector.
    In which,
    CD is perpendicular bisector on AB.
    Hence,
    AD = DB
    CD = CD (common)
    ADC = BDC = 90o
    So, according to SAS rule
    ACD  BCD
    Hence,
    CA = CB
    So, triangle is always isosceles.
    Hence proved.
    • Final Answer: 
    Correct option A always.

    If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then the triangle is ____ isosceles.

    Maths-General
    Answer:
    • Hints:
    • Perpendicular bisector theorem
    • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step by step explanation: 
    • Step 1:
    Let consider given figure,

    Let arbitrary point C on perpendicular bisector.
    In which,
    CD is perpendicular bisector on AB.
    Hence,
    AD = DB
    CD = CD (common)
    ADC = BDC = 90o
    So, according to SAS rule
    ACD  BCD
    Hence,
    CA = CB
    So, triangle is always isosceles.
    Hence proved.
    • Final Answer: 
    Correct option A always.
    General
    Maths-

    Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B. On which of the following segments must P be located?

    Answer:
    • Hints:
      • Perpendicular bisector theorem
      • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step by step explanation: 
      • Given:
    Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B.
    • Step 1:
    • In △ ABC,
    According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    So,
    As P is equidistant from A and B it lies on perpendicular bisector on AB.
    • Final Answer: 
     Correct option. B. The perpendicular bisector of 𝐴𝐵.

    Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B. On which of the following segments must P be located?

    Maths-General
    Answer:
    • Hints:
      • Perpendicular bisector theorem
      • According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    • Step by step explanation: 
      • Given:
    Point P is inside △ 𝐴𝐵𝐶 and is equidistant from points A and B.
    • Step 1:
    • In △ ABC,
    According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
    So,
    As P is equidistant from A and B it lies on perpendicular bisector on AB.
    • Final Answer: 
     Correct option. B. The perpendicular bisector of 𝐴𝐵.
    General
    Maths-

    A constant has a degree__________.

    Explanation:
    • We have been given a statement in the question for which we have to fill the blank by choosing the appropriate answer from the given four options.
    Step 1 of 1:
    The degree of a constant is Zero.
    By definition of degree we know that it is highest power of variable present in polynomial.
    But for constant there is no polynomial.
    So, The degree of constant is Zero
    Hence, Option B is correct.

    A constant has a degree__________.

    Maths-General
    Explanation:
    • We have been given a statement in the question for which we have to fill the blank by choosing the appropriate answer from the given four options.
    Step 1 of 1:
    The degree of a constant is Zero.
    By definition of degree we know that it is highest power of variable present in polynomial.
    But for constant there is no polynomial.
    So, The degree of constant is Zero
    Hence, Option B is correct.
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