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The orthocentre of the triangle formed by the lines x + y = 1, 2x + 3y = 6 and 4x – y + 4 = 0 lies in the quadrant whose number is .... |
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Answer» Solving the above equations taken two by two, the vertices of the triangle are A(-3/5,8/5), B(-3,4), and C(-3/7, 16/7) The equation of the altitude drawn from A to the side BC is y - 8/5 = 3/2(x + 3/5) 3x - 2y = -5 ....(1) Again the equation of the altitude from B onto CA is y - 4 = -1/4(x + 3) ⇒ x + 4y = 13 ...(2) Solving Eqs. (1) and (2), the coordinates of the orthocentre are (3/7,22/7) which lies in quadrant number 1. |
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