Question

find the distance between the points (0, 2) and (-10, 3). write your answer as a whole number or a fully simplified radical expression. do not round.

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, $x_1 = 0,y_1 = 2,x_2=- 10,y_2 = 3$.

Step2: Substitute values

$d=\sqrt{(-10 - 0)^2+(3 - 2)^2}=\sqrt{(-10)^2+1^2}$.

Step3: Calculate squares

$(-10)^2=100$ and $1^2 = 1$, so $d=\sqrt{100 + 1}$.

Step4: Simplify

$d=\sqrt{101}$.

Answer:

$\sqrt{101}$