Question

find the distance between the points (-1, 7) and (0, 3). write your answer as a whole number or a fully - simplified radical expression. do not round.

Explanation:

Step1: Identify 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, $x_1=-6,y_1 = 7,x_2 = 0,y_2=3$.

Step2: Substitute values

$d=\sqrt{(0 - (-6))^2+(3 - 7)^2}=\sqrt{(6)^2+(-4)^2}$.

Step3: Calculate squares

$d=\sqrt{36 + 16}$.

Step4: Add values inside square - root

$d=\sqrt{52}$.

Step5: Simplify the radical

$d=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$