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

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?

 

 

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).

 

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5 units

 

Let's try some questions like this.