Given: image of (2,1) is (5,2)
To find:
The equation of the mirror.
Explanation:
Let the image of A (2, 1) be B (5, 2).
Let M be the midpoint of AB.
Coordinates of M = \(\Big(\frac{2+5}{2},\frac{1+2}{2}\Big)\)
= \(\Big(\frac{7}{2},\frac{3}{2}\Big)\)
Diagram:
Let CD be the mirror.
The line AB is perpendicular to the mirror CD.
∴ Slope of AB × Slope of CD = − 1
⇒ Slope of CD = -3
Thus, the equation of the mirror CD is
\(y- \frac{3}{2} = -3\Big(x-\frac{7}{2}\Big)\)
⇒ 2y – 3 = -6x + 21
⇒ 6x + 2y -24 = 0
⇒ 3x + y – 12 = 0
Hence, the equation of mirror is 3x + y – 12 = 0.
