topic badge
iGCSE (2021 Edition)

11.17 Perpendicular lines (Extended)

Worksheet
Perpendicular lines (Extended)
1

Describe what it means for two lines to be perpendicular.

2

If two lines are perpendicular, state the product of their gradients.

3

State whether the following pairs of lines are perpendicular:

a

y = x + 1 and y = x - 1

b

y = 3 x - 7 and y = - 3 x + 6

c

y = - 3 x + 6 and y = \dfrac{x}{3} + 7

d

y = \dfrac{2 x}{3} + 4 and y = -1 - \dfrac{3 x}{2}

e

y = - \dfrac{x}{3} - 9 and y = - \left( 3 x - 27 \right)

f

y = 3 x - 5 and y = -\dfrac{1}{3} x + 6

g

y=-\dfrac{2x}{3}+1 and y=-1+\dfrac{3x}{2}

h

y=\dfrac{3x}{5}+6 and y=\dfrac{-5x-30}{-3}

4

Given that the following pairs of lines are perpendicular, calculate the value of m:

a

5 x + 4 y =-8 \\m x + 9 y = 8

b

- 6 x + 6 y = 8 \\ m x + 10 y =- 8

5

Find the gradient of the line perpendicular to the following lines:

a

Line with gradient 6

b
y = 6 x + 3
c
y = \dfrac{x}{8} + 3
d
y = 8 - x
6

Consider the lines L_{1}: 8 x = - 7 y + 3 and L_2: 7 y - 8 x = 7.

a

Find the gradient of line L_{1}.

b

Find the gradient of line L_{2}.

c

Are the two lines perpendicular?

7

Find the equation of a line described by the following information:

a

Perpendicular to the x-axis and passes through \left( - 8 , - 1 \right).

b

Perpendicular to the y-axis and passes through \left( - 8 , - 8 \right).

c

Perpendicular to y = - \dfrac{x}{2} + 5, and goes through the point \left(0, 6\right).

d

Perpendicular to y = 6 x + 10, and has the same y-intercept.

e

Perpendicular to the line that passes through \left(1, 1\right) and \left(3, 13\right), and has a y-intercept of \left(0, - 4 \right).

8

The line L_{1} is perpendicular to y = 5 x - 4 and cuts the y-axis at 1.

a

Find the gradient of line L_{1}.

b

Find the equation of line L_{1}.

9

The line L_{1} is perpendicular to y = 10 x + 8 and passes through the point of intersection of the lines y = x + 5 and 8 x - 10 y =- 60 .

a

Find the gradient of line L_{1}.

b

Find the point of intersection of y = x + 5 and 8 x - 10 y + 60 = 0.

c

Find the equation of the perpendicular line L_{1}.

Applications (Extended)
10

Consider the rhombus ABCD on the number plane:

a

Find the gradients of its diagonals.

i

Gradient of AC

ii

Gradient of BD

b

Are the diagonals of the rhombus perpendicular? Explain your answer.

-5
-4
-3
-2
-1
1
2
3
4
5
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
11

The four vertices of quadrilateral ABCD have been plotted on the number plane:

a

Find the gradient of the following sides:

i

AB

ii

BC

iii

DC

iv

AD

b

Given that side AB = BC, determine the type of quadrilateral described by the four points.

1
2
3
4
5
6
7
x
1
2
3
4
5
6
y
Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

0607C4.5

Gradient of parallel lines.

0607E4.5

Gradient of parallel and perpendicular lines.

What is Mathspace

About Mathspace