Answer
(a) Refer to the image below for the plot.
(b) Distance between the two points = $7\sqrt2 \approx 9.90$ units
(c) Midpoint of the segment joining the two points: $(-0.5, 1.5)$
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 distanc formula $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ to have:
$d=\sqrt{[3-(-4)]^2+(-2-5)^2}
\\d=\sqrt{(7)^2+(-7)^2}
\\d=\sqrt{49+49}
\\d=\sqrt{98}
\\d=\sqrt{49(2)}
\\d=7\sqrt2
\\d\approx 9.90$
(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 = $\left(\frac{3+(-4)}{2}, \frac{-2+5}{2}\right)=(-0.5, 1.5)$
