So for part A, you will be using the distance formula, which is [tex] \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex] . Since we know that point A is (-2,3) and point B is (6,7), we can solve for it as such:
[tex] \sqrt{(6-(-2))^2+(7-3)^2}\\ \sqrt{8^2+4^2}\\ \sqrt{64+16}\\ \sqrt{80}\\ 8.9 [/tex]
AB = 8.9 units.
For part B, you will be using the midpoint formula, which is [tex] (\frac{x_2+x_1}{2} ,\frac{y_2+y_1}{2}) [/tex] . Since we know the coordinates of point A and point B, we can solve for it as such:
[tex] (\frac{6+(-2)}{2} ,\frac{7+3}{2})\\\\ (\frac{4}{2} ,\frac{10}{2}) \\ \\ (2,5) [/tex]
The midpoint of AB is (2,5).
