Let the triangle PQR be the image of the triangle with vertices (1,3), (3,1) and (2, 4) in the line x + 2y = 2. If the centroid of $∆$ PQR is the point $(α, β)$ then 15 $(α - β)$ is equal to

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Detailed Solution

Let G be the centroid of triangle formed by (1, 3), (3, 1), and (2, 4)

$G ≅ (2, \frac{8}{3})$

Image of G w. r. t $x + 2 y - 2 = 0$

$\begin{aligned} \frac{α - 2}{1} = \frac{β - \frac{8}{3}}{2} = - 2 \frac{(2 + \frac{16}{3} - 2)}{1 + 4} \end{aligned}$

$\begin{array}{r} \Rightarrow α = \frac{- 32}{15} + 2 = \frac{- 2}{15}, β = \frac{- 32 \times 2}{15} + \frac{8}{3} = \frac{- 24}{15} \end{array}$

$15 (α - β) = - 2 + 24 = 22$

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