Question

use the distance formula to find the distance between (5, - 4) and (0, 8).

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(5, - 4)$ and $(x_2,y_2)=(0,8)$.

Step2: Apply the distance formula

The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute the values: $d=\sqrt{(0 - 5)^2+(8-( - 4))^2}$.

Step3: Simplify the expressions inside the square - root

First, $(0 - 5)^2=(-5)^2 = 25$ and $(8-( - 4))^2=(8 + 4)^2=12^2 = 144$. Then $d=\sqrt{25 + 144}$.

Step4: Calculate the sum inside the square - root and then the square - root

$25+144 = 169$, and $\sqrt{169}=13$.

Answer:

$13$