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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 × -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.