Question

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

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 8,y_1=-4,x_2 = 4,y_2 = 4$.

Step2: Substitute values

$d=\sqrt{(4 - 8)^2+(4-(-4))^2}=\sqrt{(-4)^2+(4 + 4)^2}=\sqrt{16 + 64}$.

Step3: Simplify

$d=\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}$.

Answer:

$4\sqrt{5}$