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**

Answers:

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.