Question

find the distance between the points (8, 0) and (3, 4). 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: Assign the values of the points

Let $(x_1,y_1)=(8,0)$ and $(x_2,y_2)=(3,4)$. Then $x_2 - x_1=3 - 8=-5$ and $y_2 - y_1=4 - 0 = 4$.

Step3: Calculate the squares

$(x_2 - x_1)^2=(-5)^2 = 25$ and $(y_2 - y_1)^2=4^2 = 16$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 16=41$.

Step5: Find the distance

$d=\sqrt{41}$.

Answer:

$\sqrt{41}$