Question

find the distance between the points (3, 9) and (8, 0). write your answer as a whole number or a fully simplified radical expression. do not round. \sqrt{\box} units

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Here, \( (x_1, y_1)=(3, 9) \) and \( (x_2, y_2)=(8, 0) \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1 = 8 - 3 = 5 \) and \( y_2 - y_1 = 0 - 9 = -9 \). Then, substitute these into the formula: \( d=\sqrt{(5)^2+(-9)^2} \).

Step3: Simplify the expression inside the square root

Calculate \( (5)^2 = 25 \) and \( (-9)^2 = 81 \). Then, add them together: \( 25 + 81 = 106 \). So, \( d = \sqrt{106} \).

Answer:

\( \sqrt{106} \)