Question

find the distance between the points (1, 3) and (3, 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 $x_1 = 1,y_1 = 3,x_2=3,y_2 = 10$.

Step2: Substitute values

$d=\sqrt{(3 - 1)^2+(10 - 3)^2}=\sqrt{2^2+7^2}$.

Step3: Calculate squares

$d=\sqrt{4 + 49}=\sqrt{53}$.

Answer:

$\sqrt{53}$