Question

find the distance between the points (8, 9) and (10, 1). write your answer as a whole number or a fully simplified radical expression. do not round.

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: Substitute the given points

Let $(x_1,y_1)=(8,9)$ and $(x_2,y_2)=(10,1)$. Then $x_2 - x_1=10 - 8 = 2$ and $y_2 - y_1=1 - 9=-8$.

Step3: Calculate the squares

$(x_2 - x_1)^2=2^2 = 4$ and $(y_2 - y_1)^2=(-8)^2 = 64$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 64=68$.

Step5: Find the square - root

$d=\sqrt{68}=\sqrt{4\times17}=2\sqrt{17}$.

Answer:

$2\sqrt{17}$