Question

find the distance between the two points in simplest radical form. (-8,7) and (-4,5)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-8,7)\) and \((x_2,y_2)=(-4,5)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(-4-(-8))^2+(5 - 7)^2}\)

Step3: Simplify the expressions inside the square - root

\(-4-(-8)=-4 + 8=4\) and \(5 - 7=-2\)
So \(d=\sqrt{4^2+(-2)^2}=\sqrt{16 + 4}\)

Step4: Calculate the sum inside the square - root

\(16+4 = 20\)
So \(d=\sqrt{20}\)

Step5: Simplify the radical

\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\)

Answer:

\(2\sqrt{5}\)