Question

find the distance between the points (6, 7) and (4, 2). 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, $x_1 = 6,y_1 = 7,x_2 = 4,y_2 = 2$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=4 - 6=-2$ and $y_2 - y_1=2 - 7=-5$.

Step3: Square the differences

Square the results from Step 2. $(-2)^2 = 4$ and $(-5)^2 = 25$.

Step4: Sum the squared - differences

Add the squared differences: $4 + 25=29$.

Step5: Find the square - root

$d=\sqrt{29}$

Answer:

$\sqrt{29}$