Question

find the distance between the points (4, 5) and (6, 1). 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, $x_1 = 4,y_1 = 5,x_2=6,y_2 = 1$.

Step2: Substitute values

$d=\sqrt{(6 - 4)^2+(1 - 5)^2}=\sqrt{2^2+( - 4)^2}$.

Step3: Calculate squares

$d=\sqrt{4 + 16}$.

Step4: Simplify

$d=\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$.

Answer:

$2\sqrt{5}$