Question

find the distance between the points (3, 4) and (7, 7). 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, $x_1 = 3,y_1 = 4,x_2=7,y_2 = 7$.

Step2: Substitute values

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

Step3: Calculate squares and sum

$d=\sqrt{16 + 9}=\sqrt{25}$.

Step4: Simplify radical

$d = 5$.

Answer:

5