Answer
(a) Refer to the image below for the plot.
(b) Distance between the two points =$4\sqrt{10}\approx 12.65$ units
(c) Midpoint of the segment joining the two points: $(0, 0)$
Work Step by Step
(a) Refer to the attached image in the answer part for the plot.
(b) Solve for the distance between the two points using the distance formula $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ to have:
$d=\sqrt{[6-(-6)]^2+(-2-2)^2}
\\d=\sqrt{12^2+(-4)^2}
\\d=\sqrt{144+16}
\\d=\sqrt{160}
\\d=\sqrt{16(10)}
\\d=4\sqrt{10}
\\d\approx 12.65$
(c) Find the mmidpoint of the segment that joins them by using the midpoint formula: $\text{midpoint}=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$
Midpoint = $\left(\frac{6+(-6)}{2}, \frac{-2+2}{2}\right)=(0,0)$