Mathematics
Grade-8
Easy

Question

text  The slope of the line equation joining  end text left parenthesis square root of 2 comma 5 square root of 2 right parenthesis text  and  end text left parenthesis square root of 8 comma 2 square root of 8 right parenthesis text  is  end text

  1. 1
  2. - 1
  3. 0
  4. 7

hintHint:

A line is a one-dimensional figure, which is consists of a set of points and it has no end points. Line is also known as the shortest distance between two points. Line can be expressed in form of an equation whose standard form is y=mx+c, where m is the slope of the line and c is the intercept of the line. Here, we have to write the slope of the line which can be done by using the points given in the question.

The correct answer is: - 1


    In the question the given points are open parentheses square root of 2 comma 5 square root of 2 close parentheses and open parentheses square root of 8 comma 2 square root of 8 close parentheses.
    We have to find the slope of the line joining the given points.
    We can write open parentheses square root of 8 comma 2 square root of 8 close parentheses as open parentheses 2 square root of 2 comma 4 square root of 2 close parentheses. (Since square root of 8 equals 2 square root of 2).
    Let open parentheses square root of 2 comma 5 square root of 2 close parentheses space a n d space open parentheses 2 square root of 2 comma 4 square root of 2 close parentheses space b e space open parentheses x subscript 1 comma y subscript 1 close parentheses space a n d space open parentheses x subscript 2 comma y subscript 2 close parentheses space r e s p e c t i v e l y.
    Put the values of x subscript 1 comma space x subscript 2 comma space y subscript 1 space a n d space y subscript 2 space end subscript i n space m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction.
    m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction
rightwards double arrow m equals fraction numerator 5 square root of 2 minus 4 square root of 2 over denominator 2 square root of 2 minus square root of 2 end fraction
rightwards double arrow m equals fraction numerator square root of 2 over denominator square root of 2 end fraction
rightwards double arrow m equals 1
    So, the slope joining the points open parentheses square root of 2 comma 5 square root of 2 close parentheses space a n d space open parentheses square root of 8 comma 2 square root of 8 close parentheses is 1.
    Therefore the correct option is a,i.e., 1.

    Slope of a line shows the inclination of a line. We can find the slope of a line using the points of the line using the formula m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction, where m is the slope of the line, x subscript 1 comma space y subscript 1 comma space x subscript 2 space a n d space y subscript 2 are the coordinates of the two points.

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