Question

The orthocenter of the triangle formed by the lines x + 2y = 0, 4x + 3y= 5
and 3x + y = 0​

Answer 1

Answer:

Given equations are:

x+2y=0......(1)

4x+3y−5=0.......(2)

3x+y=0..........(3)

Solving (1) and (2), vertex A=(0,0)

Solving (1) and (3), vertex B=(2,−1)

Equation of BC is 4x+3y−5=0

AB is perpendicular to BC and passes through A=(0,0)

Equation of AB is 3x−4y=0........(4)

BE is perpendicular to AC

Therefore equation of BE is x−3y=k

BE passes through B=(2,−1)

2+3=k⇒k=5

Equation of BE is x−3y=5........(5)

Solving (4) and (5)

Orthocenter is O(−4,−3)

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