Question

find the distance between the pair of points. (-8,3) and (1,-6) the distance, d, is (type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-8,3)\) and \((x_2,y_2)=(1,-6)\)

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

Substitute the values: \(d=\sqrt{(1-(-8))^2+(-6 - 3)^2}\)

Step3: Simplify the expressions inside the square root

\(1-(-8)=1 + 8=9\) and \(-6-3=-9\)
So \(d=\sqrt{9^2+(-9)^2}=\sqrt{81 + 81}\)

Step4: Calculate the sum and simplify the square root

\(81+81 = 162\), and \(d=\sqrt{81\times2}=\sqrt{81}\times\sqrt{2}=9\sqrt{2}\)

Answer:

\(9\sqrt{2}\)