Question

find the distance between the points (1, 10) and (5, 5). 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, \( x_1 = 1 \), \( y_1 = 10 \), \( x_2 = 5 \), \( y_2 = 5 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1=5 - 1 = 4 \)
\( y_2 - y_1=5 - 10=- 5 \)

Then, substitute these into the distance formula:
\( d=\sqrt{(4)^2+(-5)^2} \)

Step3: Simplify the expression inside the square root

Calculate \( (4)^2 = 16 \) and \( (-5)^2 = 25 \).
So, \( d=\sqrt{16 + 25} \)
\( d=\sqrt{41} \)

Answer:

\(\sqrt{41}\)