In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)
Just draw a picture of what is being described. A perpendicular bisector:
-- intersects at the midpoint
-- forms a right angle
Here's my rudimentary drawing:
Looking at the drawing above, we can see that point C must have a positive x-coordinate and a negative y-coordinate.
Eliminate A, B and E.
Since point C is further to the right than is point A, the x-coordinate of point C must be greater than 2.
Eliminate C.
The correct answer is
D.
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