Question

Find the distance between the two points in simplest radical form.

Answer 1

The distance between the two points is $2\sqrt{5}$

Explanation:

Given that the two points are $(-8,-2)$ and $(-6,2)$

We need to determine the distance between the two points in simplest radical form.

The distance between the two points can be determined using the distance formula,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let us substitute the coordinates $(-8,-2)$ and $(-6,2)$ in the above formula, we get,

$d=\sqrt{(-6+8)^2+(2+2)^2}$

Simplifying the terms, we get,

$d=\sqrt{(2)^2+(4)^2}$

Squaring the terms, we get,

$d=\sqrt{4+16}$

Adding, we get,

$d=\sqrt{20}$

Simplifying, we have,

$d=2\sqrt{5}$

Thus, the distance between the two points in simplest radical form is $2\sqrt{5}$