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:
[tex] x_m = \dfrac{x_1 + x_2}{2}~~~and~~~y_m = \dfrac{y_1 + y_2}{2} [/tex]
[tex] 0 = \dfrac{-5 + x_2}{2}~~~and~~~0 = \dfrac{4 + x_2}{2} [/tex]
[tex] 0 = -5 + x_2~~~and~~~0 = 4 + x_2 [/tex]
[tex] -x_2 = -5~~~and~~~-4 = x_2 [/tex]
[tex] x_2 = 5~~~and~~~x_2 = -4 [/tex]
Answer: B(5, -4)
As you can see, both methods give you the same answer.
