Question

find the distance between the points (6, 4) and (2, 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, $(x_1,y_1)=(6,4)$ and $(x_2,y_2)=(2,3)$.

Step2: Substitute values

$d=\sqrt{(2 - 6)^2+(3 - 4)^2}=\sqrt{(-4)^2+(-1)^2}$.

Step3: Calculate squares

$d=\sqrt{16 + 1}$.

Step4: Simplify

$d=\sqrt{17}$.

Answer:

$\sqrt{17}$