Question

Point A is at (-2, 4) and point M is at (2.5, 3.5).

Point M is the midpoint of point A and point B.
What are the coordinates of point B?

Answer 1

Coordinates of point B: (7, 3)

Step-by-step explanation:

Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),

Rewrite the equation to find the coordinates of B

Coordinates of point B: (7, 3)

Answer 2

Coordinates of point B: (7, 3)

Explanation:

Given M(2.5, 3.5) as midpoint of AB, and A(-2, 4),

let
`A(-2, 4) = (x_2, y_2)`

`B(?, ?) = (x_1, y_1)`

`M(2.5, 3.5) = ((x_1 +(-2))/(2), (y_1 +(4))/(2))`

Rewrite the equation to find the coordinates of B

`2.5 = (x_1 - 2)/(2)` and
`3.5 = (y_1 + 4)/(2)`

Solve for each:

`2.5 = (x_1 - 2)/(2)`

`2.5*2 = (x_1 - 2)/(2)*2`

`5 = x_1 - 2`

`5 + 2 = x_1 - 2 + 2`

`7 = x_1`

`x_1 = 7`

`3.5 = (y_1 + 4)/(2)`

`3.5*2 = (y_1 + 4)/(2)*2`

`7 = y_1 + 4`

`7 - 4 = y_1 + 4 - 4`

`3 = y_1`

`y_1 = 3`

Coordinates of point B: (7, 3)