Perpendicular Line Formula

Perpendicular Line Formula

A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.

Consider the equation of the line is ax + by + c = 0 and coordinates are (x1, y1), the slope should be − a/b. If one line is perpendicular to this line, the product of slopes should be -1. Let m1 and m2 be the slopes of two lines, and if they are perpendicular to each other, then their product will be -1.

PerpendicularLines;m1×m2=−1

Slopem=−ab

PerpendicularLineequation:(y−y1)=m(x−x1)

Solved Example

Question: Check whether 2x + 3y + 5 = 0 and 3x – 2y + 1 = 0 are perpendicular or not.

Solution:

The given equations of lines are:
2x + 3y + 5 = 0 and 3x â€“ 2y + 1 = 0

To check whether they are perpendicular to each other, find out the slopes of both lines. If the product of their slopes is -1, these lines are perpendicular to each other.

Slope formula is; m =

−ab

Slope for first line,

m1
=
−ab
=
−23
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Slope for second line,

m2
−ab
=
−3−2

m1×m2
=
−23
×
−3−2
= -1

Since the product of slope is -1, the given lines are perpendicular to each other.

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