1.

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 ....

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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