Question

find the distance between the two points. simplify your answers. and write the exact answer in simplest radical form for irrational answers. (5, -5) and (-5, 5)

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, $x_1 = 5,y_1=-5,x_2=-5,y_2 = 5$.

Step2: Substitute values

$d=\sqrt{(-5 - 5)^2+(5-(-5))^2}=\sqrt{(-10)^2+(10)^2}$.

Step3: Calculate squares

$d=\sqrt{100 + 100}=\sqrt{200}$.

Step4: Simplify radical

$d=\sqrt{100\times2}=10\sqrt{2}$.

Answer:

$10\sqrt{2}$