HELP ME! Beginners geometry!

A rhombus is centered on the origin. One side of the rhombus goes through the points (a, 0) and (0, b). What are possible coordinates for one of the other sides?


A.
(–a, 0), (a, 0)





B.

(b, 0), (0, –a)





C.

(0, –b), (0, b)





D.

(–a, 0), (0, –b)

since both vertex in the X axis must be at the same distance from the Y axis, you can easily notice that if one vertex is located in x=a, then its opposite must be in x=-a;
then, the same happens with the other 2 verteces, so if one vertex is in y=b, then necessarily its opposite must be in y=-b (remember that the figure is centered in (0,0)

so: (a,0) (-a,0) (0,b) (0,-b)

D

D

D (-a,0) and(0,-b)