Question

what is the distance between (-2, 2) and (2, 8)?
none of these
2√13
4√26
2√26

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, \((x_1, y_1)=(-2, 2)\) and \((x_2, y_2)=(2, 8)\).

Step3: Substitute into the formula

First, calculate \( x_2 - x_1 = 2 - (-2)=4 \) and \( y_2 - y_1 = 8 - 2 = 6 \).
Then, \( d=\sqrt{(4)^2+(6)^2}=\sqrt{16 + 36}=\sqrt{52} \).

Step4: Simplify the radical

Simplify \( \sqrt{52} \). We know that \( 52 = 4\times13 \), so \( \sqrt{52}=\sqrt{4\times13}=\sqrt{4}\times\sqrt{13}=2\sqrt{13} \).

Answer:

$2\sqrt{13}$ (corresponding to the option "2√13")