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

Question

Philoid · Accepted Answer

The equation of the given line is

x +3y = 7

Let point B (a, b) be the image of point A (3, 8)

So, line (1) is the perpendicular bisector of AB.

Slope of AB = , while the slope of the line (1) =

Since, line (1) is perpendicular to AB.

=> b – 8 = 3a – 9

=> 3a – b = 1 --------------- (2)

Mid – point of AB =

The mid – point of line segment AB will also satisfy line (1).

Thus, from equation (1), we get,

⇒ a + 3 + 3b + 24 = 14

⇒ a + 3b = -13 -------------(3)

On solving equations (2) and (3), we get, a = -1 and b = -4

Therefore, the image of the given point with respect to the given line is (-1, -4).