Q. 183.9( 31 Votes )
Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror.
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).
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