Question

If the image of the point (2,1) with respect to the line mirror be (5, 2). Find the equation of the mirror.

Answer 1

Let CD be the line mirror with slope m_1.

Now the slope of the line joining A(2, 1) and B(5, 2).
m₂ = `(2 - 1)/(5 - 2) = (1)/(3)`
Since CD ⊥ AB
So, m₁m₂ = -1
⇒ `m_1 xx (1)/(3)` = -1
⇒ m₁ = -3.
Now mid point of AB = `((2+ 5)/2, (1 + 2)/2) = (7/2, 3/2)`
Equation of the mirror CD,
y = y₁ = m(x - x1)
⇒ `y - (3)/(2) = -3(x-7/2)`
⇒ `y - (3)/(2) = -3x + (21)/(2)`
⇒ 2y - 3 = -6x + 21
⇒ 6x + 2y - 3 - 21 = 0
⇒ 6x + 2y - 24 = 0
or 3x + y - 12 = 0.