Question

find the distance between the points (9, 9) and (0, 5). 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, $(x_1,y_1)=(9,9)$ and $(x_2,y_2)=(0,5)$.

Step2: Calculate differences

$x_2 - x_1=0 - 9=- 9$ and $y_2 - y_1=5 - 9=-4$.

Step3: Square the differences

$(x_2 - x_1)^2=(-9)^2 = 81$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 16=97$.

Step5: Take square - root

$d=\sqrt{97}$

Answer:

$\sqrt{97}$