Question

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

Explanation:

Step1: Identify the two points

The points are $(-1, 3)$ and $(-8, -6)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute $x_1=-1,y_1=3,x_2=-8,y_2=-6$:
$$d=\sqrt{(-8-(-1))^2+(-6-3)^2}$$

Step3: Simplify inside the square root

Calculate differences first:
$$d=\sqrt{(-7)^2+(-9)^2}=\sqrt{49+81}$$

Step4: Sum and simplify radical

$$d=\sqrt{130}$$

Answer:

$\sqrt{130}$