Question

find the distance between the points (9, 6) and (6, 10). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify the 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: Assign the values

Let $(x_1,y_1)=(9,6)$ and $(x_2,y_2)=(6,10)$. Then $x_2 - x_1=6 - 9=- 3$ and $y_2 - y_1=10 - 6 = 4$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=4^2 = 16$. The sum is $9 + 16=25$.

Step4: Find the square - root

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

Answer:

5