Question

find the distance between the points (6, 1) and (8, 10). write your answer as a whole number or a fully simplified radical expression. do not round. 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, \( x_1 = 6 \), \( y_1 = 1 \), \( x_2 = 8 \), \( y_2 = 10 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1=8 - 6 = 2 \)
\( y_2 - y_1=10 - 1 = 9 \)

Then, substitute these into the distance formula:
\( d=\sqrt{(2)^2+(9)^2} \)

Step3: Simplify the expression inside the square root

Calculate \( (2)^2 = 4 \) and \( (9)^2 = 81 \). Then add them:
\( 4 + 81=85 \)

So, \( d = \sqrt{85} \)

Answer:

\(\sqrt{85}\)