Question

find the distance between the points (0, 5) and (5, 10). write your answer as a whole number or a fully simplified radical expression. do not round. units

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, $x_1 = 0,y_1 = 5,x_2=5,y_2 = 10$.

Step2: Substitute values

$d=\sqrt{(5 - 0)^2+(10 - 5)^2}=\sqrt{5^2+5^2}$.

Step3: Calculate squares

$d=\sqrt{25 + 25}=\sqrt{50}$.

Step4: Simplify radical

$d=\sqrt{25\times2}=5\sqrt{2}$ units.

Answer:

$5\sqrt{2}$ units