Answer:
Coordinates of M = (2, -1)
Length of AB = 10 units
Step-by-step explanation:
Coordinates of the midpoint (M) of the distance between A(2, 4) and B(2, -6)
[tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex]
Let [tex] A(2, 4) = (x_1, y_1) [/tex]
[tex] B(2, -6) = (x_2, y_2) [/tex]
Thus:
[tex] M(\frac{2 + 2}{2}, \frac{4 +(-6)}{2}) [/tex]
[tex] M(\frac{4}{2}, \frac{-2}{2}) [/tex]
[tex] M(2, -1) [/tex]
Length of AB:
Distance between A(2, 4) and B(2, -6):
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] A(2, 4) = (x_1, y_1) [/tex]
[tex] B(2, -6) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(2 - 2)^2 + (-6 - 4)^2} [/tex]
[tex] AB = \sqrt{(0)^2 + (-10)^2} [/tex]
[tex] AB = \sqrt{0 + 100} = \sqrt{100} [/tex]
[tex] AB = 10 [/tex]
