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A line L reflects point P(2, 3) to Q(4, 5). Under reflection in the same line L, what is the image of the point R(0, 0)?

1. (2, 2)
2. (4, 5)
3. (3, 4)
4. (7, 7)

Correct answer: (7, 7)

Solution

L is the perpendicular bisector of PQ: midpoint (3,4), slope -1, so x+y=7. Reflecting (0,0) in x+y=7 gives (7,7).

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