Robinson Tuition
Grade 7 · Higher · free GCSE maths worksheet

Perpendicular lines

Gradients that multiply to -1.

13 original questions, 44 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

For each pair of lines, decide whether they are perpendicular. You must show your working.

  1. y = 4x + 1   and   4y + x = 8
  2. y = 2x + 5   and   2y = x − 3
3 marks
Show answer
a) Yes b) No
2

The line y = ax + 5 is perpendicular to the line by = 3x − 2.

Find b in terms of a.

3 marks
Show answer
b = -3a
3

The line l passes through the points (−1, 2) and (3, 10).

Find the equation of the line perpendicular to l that passes through the point (4, 5). Give your answer in the form y = mx + c.

3 marks
Show answer
y = -1/2 x + 7
4

A straight line has equation y = 4x + 3

Write down the gradient of a line perpendicular to this line.

1 mark
Show answer
-14
5

The line L is perpendicular to the line with equation y = 2x − 3

L passes through the point (4, 1).

Find an equation of L.

3 marks
Show answer
y = -x2 + 3
6

Find the equation of the straight line that is perpendicular to y = 2x - 3 and passes through the point (4, 1).

3 marks
Show answer
y = -x2 + 3
7

The straight line L has equation y = -x3 + 5

Find the equation of the straight line that is perpendicular to L and passes through the point (2, -1).

3 marks
Show answer
y = 3x - 7
8

The straight line L1 has equation y = px + 4, where p is a constant.

The straight line L2 has equation 2x + 6y = 9

L1 is perpendicular to L2

Find the value of p.

3 marks
Show answer
p = 3
9

The straight line L1 has equation y = 2x + 6

L1 crosses the x-axis at the point A and crosses the y-axis at the point B.

The straight line L2 is perpendicular to L1 and passes through B.

L2 crosses the x-axis at the point C.

Work out the area of triangle ABC.

xyL₁L₂OABCDiagram NOT accurately drawn
5 marks
Show answer
45
10

A is the point (0, 2) and B is the point (8, 6).

The point M lies on AB so that AM : MB = 1 : 3

Find the equation of the straight line that passes through M and is perpendicular to AB.

5 marks
Show answer
y = -2x + 7
11

A is the point (−1, 3) and B is the point (5, 7).

Find the equation of the perpendicular bisector of AB. Give your answer in the form y = mx + c.

4 marks
Show answer
y = -3/2 x + 8
12

ABCD is a rectangle, with the vertices in order. A is (1, 2), B is (5, 4) and C is (7, 0).

  1. Show that angle ABC = 90°.
  2. Work out the coordinates of D.
4 marks
Show answer
a) gradients 1/2 and -2, product -1 b) (3, -2)
13

Line L1 passes through (0, 1) and (1, k + 1).

Line L2 passes through (0, 0) and (1, k − 4).

L1 and L2 are perpendicular.

Show that k2 − 4k + 1 = 0 and hence find the possible values of k, giving your answers as surds.

4 marks
Show answer
k = 2 + sqrt(3) or k = 2 - sqrt(3)

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

All Grade 7 topics