JEE Main 2024 Mathematics question
The equations of two sides AB and AC of a triangle ABC are 4x + y = 14 and 3x − 2y = 5, respectively. The point divides the third side BC internally in the ratio 2 : 1. The equation of the side BC is:
Answer: (C)
Solution
Let B = (b, 14 − 4b) on AB and C = (c, (3c − 5)/2) on AC. The point P(2, −4/3) divides BC internally in the ratio 2 : 1 (from B), so P = (B + 2C)/3: b + 2c = 6 and (14 − 4b) + (3c − 5) = −4,
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