Question

Find the orthocenter of the triangle fromed by the lines x+2y+0=0 , 4x+3y-5=0, 3x+y+0=0

Answer 1

Answer:

Orthocenter is O(−4,−3)

Step-by-step explanation:

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)