Perpendicular Lines

In this section, we will learn about perpendicular lines, how they relate to slope, and how to spot them on a graph. Understanding perpendicular lines is important in co-ordinate geometry, and we'll take it step by step to make sure it's clear and easy to follow.

What Are Perpendicular Lines?

Perpendicular lines are lines that meet or cross each other at a right angle, which is a 90-degree angle. Imagine the corner of a book or the way two streets intersect at a perfect "$T$" shape—those are examples of perpendicular lines.

Here are the key points:

• Perpendicular lines meet at a 90-degree angle.
• They form a perfect "$L$" shape where they cross.

Perpendicular Lines and Slope

To understand why perpendicular lines meet at right angles, we need to look at their slopes. The slope of a line tells us how steep the line is—whether it goes up or down as you move along it.

Here's the important rule:

• The slopes of perpendicular lines multiply together to give -1. This means that if one line has a slope $m$, and another line is perpendicular to it with slope $m'$, then:

$m \times m' = -1$

How to Spot Perpendicular Lines on a Graph

There are two main ways to recognise perpendicular lines:

1. Check the Slopes:

• If you know the equations of the lines, you can calculate their slopes. If the slopes multiply to give -1, or if one slope is the flipped and sign-changed version of the other, the lines are perpendicular.

2. Look at the Graph:

• If you're looking at a graph, perpendicular lines will always meet at a right angle. If you can see that the lines form an "$L$" shape where they cross, they are perpendicular.

Key Points to Remember

• Slopes Multiply to -1: Perpendicular lines have slopes that, when multiplied together, give -1. An easy way to remember this is to "flip it and change the sign."
• Right Angles: On a graph, perpendicular lines always meet at a 90-degree angle.
• Visual Cues: When looking at a graph, perpendicular lines will form an "$L$" shape where they meet.

Practice Identifying Perpendicular Lines

To get comfortable with this concept, try identifying perpendicular lines by finding their slopes and checking how they look on a graph. With practice, you'll be able to spot perpendicular lines quickly and easily!

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