Question

what is the distance between (-8, 0) and (4, 4)?
○ 4√10
○ 10√16
○ 4√16
○ none of these

Explanation:

Step1: Recall the distance formula

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

Step2: Identify the coordinates

Here, \( x_1 = -8 \), \( y_1 = 0 \), \( x_2 = 4 \), \( y_2 = 4 \).

Step3: Substitute into the formula

First, calculate \( x_2 - x_1 = 4 - (-8) = 12 \) and \( y_2 - y_1 = 4 - 0 = 4 \).
Then, \( d = \sqrt{(12)^2 + (4)^2} = \sqrt{144 + 16} = \sqrt{160} \).

Step4: Simplify the square root

Simplify \( \sqrt{160} \): \( \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10} \).

Answer:

A. \( 4\sqrt{10} \)