Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the two points

The points are $(-7, 0)$ and $(-4, -2)$.

Step2: Recall distance formula

The distance $d$ between $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

Step3: Substitute values into formula

$$\begin{align*} d&=\sqrt{(-4-(-7))^2+(-2-0)^2}\\ &=\sqrt{(3)^2+(-2)^2} \end{align*}$$

Step4: Calculate squared terms

$$ d=\sqrt{9+4} $$

Step5: Simplify the radical

$$ d=\sqrt{13} $$

Answer:

$\sqrt{13}$