The midpoint of \overline{\text{AB}} AB is M(4, 4)M(4,4). If the coordinates of AA are (2, 1)(2,1), what are the coordinates of BB?

Answer 1

Midpoint of (x,y) of (x1,y1) and (x2,y2) = (x1 + x2 / 2, y1 + y2 /2)

so x = (x1 + x2)/2

y = (y1 + y2)/2

For (x,y) = (4,4) and (x1,y1) = (2,1):

4 = (2 + x2)/2

8 = 2 + x2

6 = x2

4 = (1 + y2)/2

8 = 1 + y2

7 = y2

so coordinates of BB are (6,7).

Answer 2

The equation for the midpoint is:

Midpoint (x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2) so we can say for the x-coordinate:

4 = (2 + x)/2

4•2 = 2 + x

8 -2 = x

x = 6

For the y-coordinate, we can say:

4 = (1 + y)/2

4•2 = 1 + y

8 - 1 = y

y = 7

So B is at (6, 7)