Question

find the distance between the two points in simplest radical form. (8, -4) and (3, 8)

Explanation:

Step1: Recall distance formula

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

Step2: Assign coordinates

Let $(x_1,y_1)=(8,-4)$ and $(x_2,y_2)=(3,8)$

Step3: Substitute into formula

$d=\sqrt{(3-8)^2+(8-(-4))^2}$

Step4: Simplify inside the root

$d=\sqrt{(-5)^2+(12)^2}=\sqrt{25+144}$

Step5: Calculate final radical

$d=\sqrt{169}=13$

Answer:

13