Answer
distance between the two given points = 10
midpoint of the segment joining the two points: $(1, 0)$
Work Step by Step
RECALL:
(i) The distance, d, between the points (a, b) and (c, d) can be found using the distance formula:
$\\d=\sqrt{(a-c)^2+(b-d)^2}$
(ii) The midpoint of the points (a, b) and (c, d) can be found using the midpoint formula:
$\\\text{midpoint} = \left(\frac{a+c}{2}, \frac{b+d}{2}\right)$
The two points are (-3, 3) and (5, -3).
Use the formulas above to have:
(a) distance between the two points:
$=\sqrt{(-3-5)^2+[3-(-3)]^2}
\\=\sqrt{(-8)^2+(6)^2}
\\=\sqrt{64+36}
\\=\sqrt{100}
\\=10$
(b) midpoint of the segment that joins them:
$\\=\left(\frac{-3+5}{2}, \frac{3+(-3)}{2}\right)
\\=\left(\frac{2}{2}, \frac{0}{2}\right)
\\=(1, 0)$