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Jee Main 2025 — Medium JEE math MCQ

Let \( ABC \) be a triangle formed by the lines \( 7x - 6y + 3 = 0, x + 2y - 31 = 0 \) and \( 9x - 2y - 19 = 0 \). Let the point \((h, k)\) be the image of the centroid of \( \Delta ABC \) in the line \( 3x + 6y - 53 = 0 \). Then \( h^2 + k^2 + hk \) is equal to:
  1. A. \quad 47 \\
  2. B. \quad 36 \\
  3. C. \quad 47 \\
  4. D. \quad 40 \\

Solution

The correct option is **B**. (B. \quad 36 \\)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let ABC ABC be a triangle formed by the lines 7x−6y+3=0,x+2y−31=0 7x - 6y + 3 = 0, x + 2y - 31 = 0 and 9x−2y−19=0 9x - 2y - 19 = 0 . Let the point (h,k)(h, k) be the image of the centroid of ΔABC \Delta ABC in the line 3x+6y−53=0 3x + 6y - 53 = 0 . Then h2+k2+hk h^2 + k^2 + hk is equal to:
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep