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Solution


Q.

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:          [2025]
1 19  
2 24  
3 21  
4 22  

Ans.

(4)

Let P, Q and R be the mirror images of points (1, 3), (3, 1) and (2, 4) in the line x + 2y – 2 = 0.

Coordinates of P is given by

x–11=y–32=–2(1+6–25) i.e., P(–1,–1)

Similarly, Q(95,–75) and R(–65,–125)

Centroid of △PQR=(–215,–85)

∴  α=–215 and β=––85

Thus, 15(α–β)=15(–215+85)=22.