Question

find the distance between the two points in simplest radical form. (-8,-9) and (-6,-5)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-8,-9)\) and \((x_2,y_2)=(-6,-5)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(-6-(-8))^2+(-5 - (-9))^2}\)

Step3: Simplify the expressions inside the square - root

\(-6-(-8)=-6 + 8=2\) and \(-5-(-9)=-5 + 9 = 4\)
So \(d=\sqrt{2^2+4^2}\)

Step4: Calculate the squares

\(2^2 = 4\) and \(4^2=16\)
Then \(d=\sqrt{4 + 16}\)

Step5: Add the numbers inside the square - root

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

Step6: Simplify the radical

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

Answer:

\(2\sqrt{5}\)