JEE Main 2024 Mathematics question
Let A(a, b), B(3, 4) and C(−6, −8) respectively denote the centroid, circumcentre and orthocenter of a triangle. Then, the distance of the point P(2a + 3, 7b + 5) from the line 2x + 3y − 4 = 0 measured parallel to the line x − 2y − 1 = 0 is
Answer: (A)
Solution
The centroid divides the line from the orthocentre to the circumcentre in the ratio 2 : 1 (orthocentre to circumcentre), so a = (2 × 3 − 6)/3 = 0 and b = (2 × 4 − 8)/3 = 0. So P = (3,
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