Question

find the distance between the points (4, 3) and (1, 5). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(4,3)$ and $(x_2,y_2)=(1,5)$. Then $x_2 - x_1=1 - 4=-3$ and $y_2 - y_1=5 - 3 = 2$.

Step3: Substitute into formula

$d=\sqrt{(-3)^2+2^2}=\sqrt{9 + 4}=\sqrt{13}$.

Answer:

$\sqrt{13}$