Question on graphing functions practice problem

GRE Quant Problem Solving
1

In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
A) (r,s)
B) (s,-r)
C) (-s,-r)
D) (-r,s)
E) (-r,-s)

Solution: Greg choose (2,3) as P and so the Q would be (-2,-3), hence choosing E) (-r, -s) as the answer.

But suppose we pick the point (5,0) as P then Q would be (-5,0). With this could D) (-r, s) be the answer too ?

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3

I think choosing number is a trap for this question as the question is asking to consider all cases (that’s why they use variables as coordinate and not some numbers)

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4

Mid point is of P(x1, y1) and Q(x2, y2) is O(x1+x2/2, y1+y2/2). So if O is (0, 0) then x1+x2=0, y1+y2=0. This means x2=-x1, y2=-y1 and in the context of question it will be (-r, -s).

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