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JEE MainMathematicsStraight Lines

In a triangle ABC , the vertex A is (2, 5) , the centroid G is (4, 3) , and the circumcenter O is (2, 1) . The equation of the straight line containing the side BC is:

Options

  1. A3x + y - 17 = 0
  2. Bx - 3y + 1 = 0
  3. C3x + y - 11 = 0
  4. D3x - y - 25 = 0

Correct answer

A. 3x + y - 17 = 0

Step-by-step solution

Let the midpoint of the side BC be M(x_m, y_m) . The centroid G divides the median AM in the ratio 2:1 . Using the section formula for A(2, 5) and G(4, 3) : 4 = 2x_m + 2 3 12 = 2x_m + 2 x_m = 5 3 = 2y_m + 5 3 9 = 2y_m + 5 y_m = 2 Thus, M (5, 2) . The circumcenter O(2, 1) lies on the perpendicular bisector of BC . Therefore, the line OM is perpendicular to BC . The slope of OM is: m_ OM = 1 - 2 2 - 5 = -1 -3 = 1 3 Since BC is perpendicular to OM , the slope of BC is: m_ BC = -3 The equation of the line containing BC

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