# 7.02 Distances in the plane using the Pythagorean theorem

## Interactive practice questions

Use the triangle and Pythagoras' theorem to complete the following:

a

Complete the equations:

$AC^2=9$AC2=9 $+$+ $\editable{}$

$AC^2$AC2 $=$= $\editable{}$

b

Hence find the length of $AC$AC in simplest radical form.

Easy
Approx 2 minutes

The points $P$P $\left(-3,-2\right)$(3,2), $Q$Q $\left(-3,-4\right)$(3,4) and $R$R $\left(1,-4\right)$(1,4) are the vertices of a right triangle, as shown on the number plane.

Consider the interval $AB$AB on the graph.

How far is the given point $P$P$\left(-15,8\right)$(15,8) from the origin?

### Outcomes

#### 8.GM.9

Apply the pythagorean theorem to find the distance between two points in a coordinate plane.