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:
Step-by-Step Solution
Key Concept: Apply the core result for lines, slopes and distances and simplify using the given constraints.
(2) 9 + 3 + 5 11 + 4 + 13 \therefore centroid of △ABC = ( , ) 3 3 17 28 = ( , ) 3 3 Let image of centroid with respect to line mirror is (h, k) 28 ⎛ k - ⎞ 1 3 \therefore (- ) = -1 ⎝ h - 17 ⎠ 2 3 17 k+28 ⎛ h + ⎞ ⎛ ⎞ 3 3 &3 + 6 ⋅ = 53 ⎝ 2 ⎠ ⎝ 2 ⎠ Solving (1) \& (2) we get h = 3, k = 4 2 2 \therefore h + k + hk = 37
Correct Answer: 2