find endpoint from midpoint and endpoint

Question

The midpoint of AB is M(3,3). If the coordinates of A are (2,-1), what are the coordinates of B?

Answer 1

The average (mean) of the x values of point A and point B must equal 3 (the x value of the midpoint). The average of the y values of point A and point B must equal 3 (the y value of the midpoint). B is (4, 7). Check the math: (2+4)/2 = 3 and (-1+7)/2 = 3.

Answer 2

Midpoint formula => M = (A+B)/2

let the coordinates of M be (X,Y)

coordinates of A be (x1,y1)

coordinates of B be (x2,y2)

(X, Y) = (3, 3)

(x1, y1) = (2, -1)

X = (x1 + x2) / 2

3 = (2 + x2) / 2

6 = 2 + x2

x2 = 6 - 2

x2 = 4

Y = (y1 + y2) / 2

3 = (-1 + y2) / 2

6 = -1 + y2

y2 = 6 + 1

y2 = 7

B = (4, 7)