Question

find the distance between the points (3, 2) and (10, 7). write your answer as a whole number or a fully simplified radical expression. do not round. units

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: Substitute the given points

Here, $x_1 = 3,y_1 = 2,x_2=10,y_2 = 7$. So $d=\sqrt{(10 - 3)^2+(7 - 2)^2}$.

Step3: Calculate the values inside the square - root

First, $(10 - 3)^2=7^2 = 49$ and $(7 - 2)^2=5^2 = 25$. Then $d=\sqrt{49 + 25}$.

Step4: Simplify the square - root

$d=\sqrt{74}$.

Answer:

$\sqrt{74}$