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

Answer:

Coordinates of point B: (7, 3)

Step-by-step explanation:

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

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

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

$M(2.5, 3.5) = (\frac{x_1 +(-2)}{2}, \frac{y_1 +(4)}{2})$

Rewrite the equation to find the coordinates of B

$2.5 = \frac{x_1 - 2}{2}$ and $3.5 = \frac{y_1 + 4}{2}$

Solve for each:

$2.5 = \frac{x_1 - 2}{2}$

$2.5*2 = \frac{x_1 - 2}{2}*2$

$5 = x_1 - 2$

$5 + 2 = x_1 - 2 + 2$

$7 = x_1$

$x_1 = 7$

$3.5 = \frac{y_1 + 4}{2}$

$3.5*2 = \frac{y_1 + 4}{2}*2$

$7 = y_1 + 4$

$7 - 4 = y_1 + 4 - 4$

$3 = y_1$

$y_1 = 3$

Coordinates of point B: (7, 3)

Answer 2

Answer:

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)