Find Perpendicular Lines

In this worksheet, students will investigate perpendicular lines and find their gradients or equations in the form of numbers or expressions.

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA,

Curriculum topic:   Algebra, Graphs of Equations and Functions

Curriculum subtopic:   Graphs Straight Line Graphs

Difficulty level:

Worksheet Overview

Perpendicular lines are lines which cross each other at a right angle.

If the gradient of a line is m, then the gradient of a perpendicular line is

When we multiply the gradients of two perpendicular lines, we get an answer of -1.

Let's see this in action now.

e.g. Find the gradient of a line which is perpendicular to a line with gradient:

a) 3

b) -1/4

c) 1.5

a) 3 × -1/3 = -1, so the gradient is =1/3

b) -1/4 × 4 = -1, so the gradient is 4

c) 1.5 × -2/3 = -1, so the gradient is -2/3

e.g. Find the gradient of a line which is perpendicular to 2y = 6x - 1.

Here we need to rearrange the equation into the form y = mx + c where m will be the gradient:

2y = 6x - 1

y = 3x - 1/2

The gradient of this line is 3.

The gradient of the perpendicular line is -1/3, because 3 × -1/3 = -1.

In this activity, we will investigate perpendicular lines and find their gradients or equations in the form of numbers or expressions.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started