Question

Complete the table below using the Midpoint and Distance Formulas.

Given: Mis the midpoint of
AB
Vertical Line Segment
Coordinates of A(2,4)
Coordinates of B(2,-6)
Coordinates of M. (_______),(_______)

Length of AB _________

Answer 1

Coordinates of M = (2, -1)

Length of AB = 10 units

Explanation:

Coordinates of the midpoint (M) of the distance between A(2, 4) and B(2, -6)

`M((x_1 + x_2)/(2), (y_1 + y_2)/(2))`

Let
`A(2, 4) = (x_1, y_1)`

`B(2, -6) = (x_2, y_2)`

Thus:

`M((2 + 2)/(2), (4 +(-6))/(2))`

`M((4)/(2), (-2)/(2))`

`M(2, -1)`

Length of AB:

Distance between A(2, 4) and B(2, -6):

`AB = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Let,

`A(2, 4) = (x_1, y_1)`

`B(2, -6) = (x_2, y_2)`

`AB = √((2 - 2)^2 + (-6 - 4)^2)`

`AB = √((0)^2 + (-10)^2)`

`AB = √(0 + 100) = √(100)`

`AB = 10`