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.

a^{2} + b^{2} = c^{2}

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?

**Answer**

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).

c^{2 }= 3^{2} + 4^{2}

c^{2} = 9 + 16

c^{2} = 25

c = √25

c =** 5 units**

Let's try some questions like this.