# Calculate the Length of a Line on a Graph Using Pythagoras' Theorem

In this worksheet, students will find the length of a line on a graph using Pythagoras' Theorem.

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Interpret Mathematical Relationships Algebraically/Geometrically

Difficulty level:

#### Worksheet Overview

In this activity, we are using what we know about Pythagoras' Theorem  to calculate the length of a line on a graph.

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

a2 + b2 = c2

Remember that the triangle must be right-angled and the hypotenuse is always the longest side and opposite the right angle.

Let's look at a typical question.

Example

What is the shortest distance between the two given points?

First, we draw a line to join the two points and then draw a vertical and horizontal line to form a right-angled triangle.

We can find the lengths of the shorter sides by counting the squares.

Now, we can use Pythagoras' Theorem to find the line length (the hypotenuse).

c2 = 32 + 42

c2 = 9 + 16

c2 = 25

c = √25

c = 5 units

Let's try some questions like this.

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