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Equations of Perpendicular Lines

In this worksheet, students find the equations of perpendicular lines.

'Equations of Perpendicular Lines' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Find the Equation of a Line

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about finding the equations of perpendicular lines.

 

Example Find the equation of the line perpendicular to
2x + 3y - 4 = 0 which goes through the point (0,-5).

 

Solution Rearrange 2x + 3y - 4 = 0 to make y the subject:
  y=
-2x
3
+
4
3
  The gradient of this line is
-2
3
(m in y=mx+c)
  The gradient of a line perpendicular to this is
3
2
.

 

The gradients of perpendicular lines have a product of -1

  ie. 
-2
3
×
3
2
= -1
  The gradient of this line is
-2
3
(compare y=mx+c)
  The gradient of a line perpendicular to this is
3
2
.

 

 

  The equation of the required line is y=
3
2
x - 5
or 2y - 3x + 10 = 0 after rearranging.

Find the equation of the line perpendicular to -6x+2y-4=0 which passes through (0,2)

Find the equation of the line perpendicular to -6x+2y-4=0 which passes through (0,4)

Find the equation of the line perpendicular to x-4y-7=0 which passes through (0,6)

Find the equation of the line perpendicular to -4x-8y+3=0 which passes through (0,4)

Find the equation of the line perpendicular to 3x+6y-5=0 which passes through (0,2)

Find the equation of the line perpendicular to 7x+y+4=0 which passes through (0,-10)

Find the equation of the line perpendicular to 9x+10y+7=0 which passes through (0, 8)

Find the equation of the line perpendicular to 9x-3y-10=0 which passes through (0, -6)

Find the equation of the line perpendicular to 2x+9y+10=0 which passes through (0, 5)

Find the equation of the line perpendicular to 2x+9y+10=0 which passes through (1, 5)

  • Question 1

Find the equation of the line perpendicular to -6x+2y-4=0 which passes through (0,2)

CORRECT ANSWER
EDDIE SAYS
-3y-x+6=0
  • Question 2

Find the equation of the line perpendicular to -6x+2y-4=0 which passes through (0,4)

CORRECT ANSWER
EDDIE SAYS
-3y-x+12=0
  • Question 3

Find the equation of the line perpendicular to x-4y-7=0 which passes through (0,6)

CORRECT ANSWER
EDDIE SAYS
y+4x-6=0
  • Question 4

Find the equation of the line perpendicular to -4x-8y+3=0 which passes through (0,4)

CORRECT ANSWER
EDDIE SAYS
-y+2x+4=0
  • Question 5

Find the equation of the line perpendicular to 3x+6y-5=0 which passes through (0,2)

CORRECT ANSWER
EDDIE SAYS
y-2x-2=0
  • Question 6

Find the equation of the line perpendicular to 7x+y+4=0 which passes through (0,-10)

CORRECT ANSWER
EDDIE SAYS
7y-x+70=0
  • Question 7

Find the equation of the line perpendicular to 9x+10y+7=0 which passes through (0, 8)

CORRECT ANSWER
EDDIE SAYS
9y-10x-72=0
  • Question 8

Find the equation of the line perpendicular to 9x-3y-10=0 which passes through (0, -6)

CORRECT ANSWER
EDDIE SAYS
9y+3x+54=0
  • Question 9

Find the equation of the line perpendicular to 2x+9y+10=0 which passes through (0, 5)

CORRECT ANSWER
EDDIE SAYS
2y-9x-10=0
  • Question 10

Find the equation of the line perpendicular to 2x+9y+10=0 which passes through (1, 5)

CORRECT ANSWER
EDDIE SAYS
2y-9x-1=0
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