# Mathematics: Perpendicular Line Formula, Solved Examples 1,2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Perpendicular Line Formula

A perpendicular line is a straight line through a point. It makes an angle of 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 and coordinates are , the slope should *be* If one line is perpendicular to this line, the product of slope should be . Let and be the slopes of two lines, then if they are perpendicular to each other.

### Solved Examples

**Question 1**: Check whether and are perpendicular or not?

**Solution**:

The given equations of lines are, and

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

Slope equation is;

Slope for first line,

Slope for second line,

So,

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

**Question 2**: Check whether and are perpendicular or not?

**Solution**: The given equations of lines are, and

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

Slope equation is;

Slope for first line,

Slope for second line,

So,

Since the product of slope is not , the given lines are not perpendicular to each other.