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Question

The orthocenter of the triangle formed by the lines x + y = 1, 2x + 3y = 6 and 4x - y + 4 = 0 lies in

A
I quadrant
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B
II quadrant
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C
III quadrant
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D
IV quadrant
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Solution

The correct option is A I quadrant
Coordinates of A and B are (-3, 4) and (35,85)​ if orthocenter P(h, k)

Then, (slope of PA)× (slope of BC) = - 1
k4h+3× 4=1

4k - 16 = -h - 3
h + 4k = 13....(i)

and slope of PB× slope of AC = - 1
k85h+35×23=1
5k85h+3×23=1
10k - 16 = 15th + 9
15th - 10k + 25 = 10
3h - 2k + 5 = 0 ...(ii)
Solving Eqs. (i) and (ii), we get h=37,k=227
Hence, orthocentre lies in I quadrant.

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