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Chapter 4: Q. 503 (page 541)

Explain in your own words why the slopes of two perpendicular lines must have opposite signs.

Short Answer

Expert verified

The slopes of two perpendicular lines must have opposite signs because the slopes of two perpendicular lines are negative reciprocal of each other.

Step by step solution

01

Step 1. Given Information  

We are given perpendicular lines.

We have to write why the slopes of two perpendicular lines must have opposite signs.

02

Step 2. Reasoning the statement

We know that the angle between two perpendicular lines is90∘.

If a line is increasing, then the slope will be positive. The perpendicular line to an increasing line must have a negative slope, otherwise, it will not intersect another line at a right angle and vice versa.

Also, the slopes of two perpendicular lines are negative reciprocal of each other.

Hence, the slopes of two perpendicular lines must have opposite signs

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