Question

find the distance between the two points in simplest radical form.
(-8, 3) and (-2, -5)

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, \(x_1=-8\), \(y_1 = 3\), \(x_2=-2\), \(y_2=-5\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=-2-(-8)=-2 + 8 = 6\)
\(y_2 - y_1=-5 - 3=-8\)
Then, substitute these into the distance formula:
\(d=\sqrt{(6)^2+(-8)^2}=\sqrt{36 + 64}\)

Step3: Simplify the expression inside the square root

\(36+64 = 100\), so \(d=\sqrt{100}\)

Step4: Evaluate the square root

\(\sqrt{100}=10\)

Answer:

The distance between the two points is \(\boxed{10}\).