Question

M is the midpoint of segment AB. A has the coordinates (-5,4) and M is at the origin. Find the coordinates of B

Answer 1

Using geometry:

Since M is the origin, point B is the mirror image of point A with respect to the origin. From the origin to point A, you go 5 units left and 4 units up. For the mirror image, start at the origin, and go 5 units right and 4 units down.

Answer: B(5, -4)

Using the midpoint formula:

`x_m = (x_1 + x_2)/(2)~~~and~~~y_m = (y_1 + y_2)/(2)`

`0 = (-5 + x_2)/(2)~~~and~~~0 = (4 + x_2)/(2)`

`0 = -5 + x_2~~~and~~~0 = 4 + x_2`

`-x_2 = -5~~~and~~~-4 = x_2`

`x_2 = 5~~~and~~~x_2 = -4`

Answer: B(5, -4)

As you can see, both methods give you the same answer.