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In an isosceles triangle ABC , the equations of the equal sides AB and AC are 2x - y = 0 and x - 2y + 3 = 0 respectively. If the centroid of the triangle is G(3,0) and p and q are the x -intercept and y -intercept of the base BC respectively, then the value of p - q is

Options

  1. A10
  2. B6
  3. C0
  4. D2

Correct answer

A. 10

Step-by-step solution

The vertex A is the intersection of the lines AB: 2x - y = 0 and AC: x - 2y + 3 = 0 . Solving these equations, we substitute y = 2x into the second equation: x - 2(2x) + 3 = 0 -3x + 3 = 0 x = 1 Then y = 2(1) = 2 . So, A (1,2) . The centroid of the triangle is given as G(3,0) . The line joining the vertex A to the centroid G is the median AD , where D is the midpoint of the base BC . The slope of the median AD is m_ AD = 0 - 2 3 - 1 = -1 . In an isosceles triangle, the median to the base is also the altitude. Theref

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