Question

find the distance between the points (8, 9) and (5, 5). 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, $x_1 = 8,y_1 = 9,x_2 = 5,y_2 = 5$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=5 - 8=- 3$ and $y_2 - y_1=5 - 9=-4$.

Step3: Square the differences

Square the results from step 2. $(-3)^2 = 9$ and $(-4)^2 = 16$.

Step4: Sum the squared - differences

Add the squared results: $9 + 16=25$.

Step5: Take the square - root

$d=\sqrt{25}=5$.

Answer:

5