Question

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

Explanation:

Step1: Identify the two points

The points are $(-8, -9)$ and $(-4, -5)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute $x_1=-8, y_1=-9, x_2=-4, y_2=-5$.

$$\begin{align*} d&=\sqrt{(-4-(-8))^2+(-5-(-9))^2}\\ &=\sqrt{(4)^2+(4)^2} \end{align*}$$

Step3: Calculate squares and sum

Compute squares, then add the results.

$$\begin{align*} d&=\sqrt{16+16}\\ &=\sqrt{32} \end{align*}$$

Step4: Simplify the radical

Factor out perfect square from 32.
$\sqrt{32}=\sqrt{16\times2}=4\sqrt{2}$

Answer:

$4\sqrt{2}$