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Question

If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.

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Solution

Let the image of A (2, 1) be B (5, 2). Also, let M be the midpoint of AB.

Coordinates of M =2+52, 1+22 =72, 32


Let CD be the mirror.
Line AB is perpendicular to the mirror CD.

Slope of AB × Slope of CD = −1

2-15-2×Slope of CD=-1Slope of CD=-3

Equation of the mirror CD:

y-32=-3x-722y-3=-6x+216x+2y-24=03x+y-12=0

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