Question

find the distance between the points (-6, -6) and (8, -8). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Recall 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 coordinates

Here, \(x_1=-6,y_1 = - 6,x_2 = 8,y_2=-8\).

Step3: Substitute into formula

Calculate \(x_2 - x_1=8-(-6)=8 + 6=14\) and \(y_2 - y_1=-8-(-6)=-8 + 6=-2\).
Then \(d=\sqrt{(14)^2+(-2)^2}=\sqrt{196 + 4}=\sqrt{200}\).

Step4: Simplify radical

\(\sqrt{200}=\sqrt{100\times2}=\sqrt{100}\times\sqrt{2}=10\sqrt{2}\).

Answer:

\(10\sqrt{2}\)