Maths-
General
Easy
Question
Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.
The correct answer is: x + y = 3 is the equation of the given line
Hint:-
1. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates. Slope = m = rise / run = y2-y1 / x2-x1
2. Parallel lines have equal slopes.
3. Equation of a line in slope point form is-
(y-y1) = m (x - x1)
Step-by-step solution:-
Let l be the line for which slope is to be found.
Comparing the equation y = x – 1 with standard form of a straight line i.e. y = mx + c, we get-
m = 1 ….................................................................................................................... (Equation i)
Now, line l is perpendicular to this line (y = x – 1) .............................................. (Given)
and we know that- Slopes of perpendicular lines are negative reciprocals of each other.
∴ Slope of line l = -1 / slope of line (y = x - 1)
∴ Slope of line l = -1 / 1 = -1 ....................... (From Equation i) ............................ (Equation ii)
We are given that line l passes through the point (1,2) and we know its slope.
i.e. x1 = 1 & y1 = 2 & m = -1
We can use slope point form of an equation to find the equation of line l-
(y - y1) = m (x - x1)
∴ (y - 2) = -1 (x - 1)
∴ y - 2 = -x + 1
∴ x + y = 1 + 2
∴ x + y = 3
Final Answer:-
∴ x + y = 3 is the equation of the given line.
Related Questions to study
Maths-
A Cylinder tank has a diameter 75 cm and height 1.8 m, Find the capacity in litres to three significant figures.
A Cylinder tank has a diameter 75 cm and height 1.8 m, Find the capacity in litres to three significant figures.
Maths-General
Maths-
Identify the line having y-intercept = 
Identify the line having y-intercept =
Maths-General
Maths-
Find the perimeter and height of an equilateral triangle whose area is equal to 60
cm2
Find the perimeter and height of an equilateral triangle whose area is equal to 60cm2
Maths-General
Maths-
A ground in a shape of a parallelogram needs to be fenced by a wire. The one side of the parallelogram is 8 inches and the area of ground is 120 sq. inches respectively.
Find the minimum length of wire needed for the work.
A ground in a shape of a parallelogram needs to be fenced by a wire. The one side of the parallelogram is 8 inches and the area of ground is 120 sq. inches respectively.
Find the minimum length of wire needed for the work.
Maths-General
Maths-
Identify the line having slope 2.
Identify the line having slope 2.
Maths-General
Maths-
Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).
Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).
Maths-General
Maths-
In the figure given below, find the area of:
(i) the shaded portion and (ii) the unshaded portion.
In the figure given below, find the area of:
(i) the shaded portion and (ii) the unshaded portion.
Maths-General
Maths-
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8m .
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1m and 1.2m and perpendicular distance between them is 0.8m .
Maths-General
Maths-
The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters (m) and two walls each of
length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of x ?
Note:
There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the
base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.
The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters (m) and two walls each of
length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of x ?
Maths-General
Note:
There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the
base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.
Maths-
The area of a trapezium is 34cm2 and the length of one of the parallel sides is 10cm and its height is 4cm. Find the length of the other parallel side.
The area of a trapezium is 34cm2 and the length of one of the parallel sides is 10cm and its height is 4cm. Find the length of the other parallel side.
Maths-General
Maths-
In the figure, ABCD is a rectangle and PQRS is a square. Find the area of the shaded portion.
In the figure, ABCD is a rectangle and PQRS is a square. Find the area of the shaded portion.
Maths-General
Maths-
A cylinder is surmounted by cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of cylinder is 6.5 cm, and the total height of structure is 12.8 cm. Find the volume of the structure.
A cylinder is surmounted by cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of cylinder is 6.5 cm, and the total height of structure is 12.8 cm. Find the volume of the structure.
Maths-General
Maths-
The scatterplot above shows the revenue, in millions of dollars, that a company carned over several years and a line of best fit for the data. In Year 4 , the difference between the actual revenue and the predicted revenue is n million dollars, where is a posative integer. What is the value of n ? Round your answer to the nearest whole number. (Disregard the 5 sign when gridding your answer.)
Note:
As we are not certain if the point of the actual revenue is exactly at the midpoint of 50 and 60, so instead of taking the midpoint 55, we can also take it to be 54 or 56.
Then the value of n can be 4 or 6 too.
The scatterplot above shows the revenue, in millions of dollars, that a company carned over several years and a line of best fit for the data. In Year 4 , the difference between the actual revenue and the predicted revenue is n million dollars, where is a posative integer. What is the value of n ? Round your answer to the nearest whole number. (Disregard the 5 sign when gridding your answer.)
Maths-General
Note:
As we are not certain if the point of the actual revenue is exactly at the midpoint of 50 and 60, so instead of taking the midpoint 55, we can also take it to be 54 or 56.
Then the value of n can be 4 or 6 too.
Maths-
Sheela wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500m2 and the perpendicular distance between the two parallel sides is 100m , find the length of the side along the river.
Sheela wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500m2 and the perpendicular distance between the two parallel sides is 100m , find the length of the side along the river.
Maths-General
Maths-
Which of the following lines pass through origin?
Which of the following lines pass through origin?
Maths-General
