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Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.

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The equation of the given line is x + 3y = 7 … (1)
Let point B (a, b) be the image of point A (3, 8).
Accordingly, line (1) is the perpendicular bisector of AB.

Since line (1) is perpendicular to AB,

The mid-point of line segment AB will also satisfy line (1).
Hence, from equation (1), we have

On solving equations (2) and (3), we obtain a = –1 and b = –4.
Thus, the image of the given point with respect to the given line is (–1, –4).

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