# Perpendicular Line Formula

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

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

\[\large Perpendicular\;Lines;\;m_{1}\times m_{2}=-1\]

\[\large Slope\;m=\frac{-a}{b}\]

\[\large Perpendicular\;Line;\; (y-y_{1})=m(x-x_{1})\]

### Solved Examples

**Question 1: **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 – 2y + 1 = 0

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

Slope equation is; m = $\frac{-a}{b}$

Slope for first line, $m_{1}$ = $\frac{-a}{b}$ = $\frac{-2}{3}$

Slope for second line, $m_{2}$ = $\frac{-a}{b}$ = $\frac{-3}{-2}$

$m_{1}\times m_{2}$ = $\frac{-2}{3}$$\times$$\frac{-3}{-2}$ = -1

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

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