Perpendicular lines. How to find the equation of a perpendicular line from another straight line graph.


To work out the equation of a line that is perpendicular to another line you will have to be given a coordinate point on the line and you will need to work out the gradient of the perpendicular line. The gradient of the perpendicular line can be worked out from the gradient of the other line by using:

m(p) = -1/m

(Note m(p) is the gradient of the perpendicular line and m is the gradient of the original line).

You can then substitute m into y = mx + c and substitute your x and y coordinates into this to work out the intercept (c).

Example 1

Work out the equation of a line perpendicular to y = 2x + 3 which passes through (-4,-5)

The gradient of the original line is 2 (m=2) so the gradient of the perpendicular line will be:

m(p) = -1/m

= -1/2

So the equation of our perpendicular line is y = -1/2x + c. All you need to do now is substitute x = -4 and y = -5 into y = -1/2x + c to work out the value of c:

-5 = -1/2 × -4 + c

-5 = 2 + c

c = -7

So the equation of the perpendicular line is y = -1/2x -7


Example 2

Work out the equation of a line perpendicular to y = -1/3x - 2 which passes through (1,2)

The gradient of the original line is -1/3 (m=-1/3), so the gradient of the perpendicular line will be:

m(p) = -1/m

= -1/(-1/3)

= 3

So the equation of our perpendicular line is y = 3x + c. All you need to do now is substitute x = 1 and y = 2 into y = -1/3x + c to work out the value of c:

2 = 3 × 1 + c

2 = 3 + c

c = -1

So the equation of the perpendicular line is y = 3x -1

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rahul0324 4 years ago from Gurgaon, India

Brilliantly explained

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