Question
The orthocenter of the triangle formed by the lines x + y = 1, 2x + 3y = 6 and 4x - y + 4 = 0 lies in
Answer: Option A
:
A
Coordinates of A and B are (-3, 4) and (−35,85) if orthocenter P(h, k)
Then, (slope of PA)× (slope of BC) = - 1
k−4h+3×4=−1
⇒ 4k - 16 = -h - 3
⇒ h + 4k = 13....(i)
and slope of PB× slope of AC = - 1
⇒k−85h+35×−23=−1
⇒5k−85h+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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:
A
Coordinates of A and B are (-3, 4) and (−35,85) if orthocenter P(h, k)
Then, (slope of PA)× (slope of BC) = - 1
k−4h+3×4=−1
⇒ 4k - 16 = -h - 3
⇒ h + 4k = 13....(i)
and slope of PB× slope of AC = - 1
⇒k−85h+35×−23=−1
⇒5k−85h+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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