Question

Use the Distance Formula to find the distance between the points $(-4,-5)$and$(5,7)$.

Short answer

The distance between the points is $15$.

Step-by-step solution

Step 1. Definition

The distance between two points $(x_1,y_1)$and $(x_2,y_2)$is given by the distance formula aslocalid="1645177038811" $d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$.

Step 2. Substitute the values in the formula

We need to find the distance between the points $(-4,-5)$and $(5,7)$.

So in the distance formula substitute $-4$for $x_1$, $-5$for $y_1$, $5$for $x_2$, and $7$for $y_2$and simplify.

$$\begin{gathered} d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2} \\ d=\sqrt{(5-{(-4))}^2+(7-{(-5))}^2} \\ d=\sqrt{9^2+{12}^2} \\ d=\sqrt{81+144} \\ d=\sqrt{225} \\ d=15 \end{gathered}$$