Problem Solving

In the rectangular coordinate system below, the line y = x is
the perpendicular bisector of segment AB (not shown), and
the y-axis is the perpendicular bisector of segment BC (not
shown). If the coordinates of point A are (3,2), what are the
coordinates of point C?
(A) (-3,-2)
(B) (-2, 3)
(C) (3,-2)
(D) (2,-3)
(E) (2, 3)

The easiest way to solve this is to draw a scaled diagram and predict each point. Doing it algebraically may take too long for test day.

Attached is a scaled diagram.

By observation, you can see clearly that in one unit square of the graph, y = x forms the diagonal, and so the other diagonal (AB) would be perpendicular to it and A and B would be equidistant from the line y = x.

Similarly, for BC to be perpendicular to y-axis and equidistant from it, simply reflect B across the y-axis to get C (-2,3)

Pick B

Thanks a lot