Question

find the distance between the points (0, 8) and (7, 4). 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, \( x_1 = 0 \), \( y_1 = 8 \), \( x_2 = 7 \), \( y_2 = 4 \).

Step2: Substitute the values into the formula

First, calculate \( (x_2 - x_1) \) and \( (y_2 - y_1) \):
\( x_2 - x_1=7 - 0 = 7 \)
\( y_2 - y_1=4 - 8=- 4 \)

Then, square these differences:
\( (x_2 - x_1)^2 = 7^2 = 49 \)
\( (y_2 - y_1)^2=(-4)^2 = 16 \)

Next, add these squared values:
\( 49+16 = 65 \)

Finally, take the square root:
\( d=\sqrt{65} \)

Answer:

\(\sqrt{65}\)