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Two vertices of a triangle are A(0, 5) and B(-4, -3) , and its orthocentre is at the origin (0, 0) . If the coordinates of the third vertex C are ( , ) , then the value of - 2 is

Options

  1. A8
  2. B0
  3. C15
  4. D12

Correct answer

D. 12

Step-by-step solution

The orthocentre H is (0, 0) and vertex A is (0, 5) . The altitude from A to the side BC passes through H . Since both A and H lie on the y-axis ( x = 0 ), the altitude AD is along the y-axis. Therefore, the side BC is perpendicular to the y-axis, which means BC is a horizontal line of the form y = k . Since vertex B(-4, -3) lies on BC , the equation of the line BC is y = -3 . Thus, the y-coordinate of C is = -3 . Next, the altitude from B to AC passes through H(0, 0) . The slope of the line BH is -3 - 0 -4 - 0 = 3

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