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प्रश्न
If the image of the point (2,1) with respect to the line mirror be (5, 2). Find the equation of the mirror.
उत्तर
Let CD be the line mirror with slope m1.
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.
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