Answer
distance between the two given points = $2\sqrt{10}$ units
midpoint of the segment joining the two given points: $(1, -2)$
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:
midpoint = $\left(\frac{a+c}{2},\frac{b+d}{2}\right)$
The two points are (-2, -3) and (4, -1).
Use the formulas above to have:
(a) distance between the two points:
$\\=\sqrt{(-2-4)^2+[(-3-(-1)]^2}
\\=\sqrt{(-6)^2+(-2)^2}
\\=\sqrt{36+4}
\\=\sqrt{40}
\\=\sqrt{4(10)}
\\=2\sqrt{10}$
(b) midpoint of the segment that joins them:
$\\=\left(\frac{-2+4}{2}, \frac{-3+(-1)}{2}\right)
\\=\left(\frac{2}{2}, \frac{-4}{2}\right)
\\=(1, -2)$
