question_answer

Let the equation of two sides of a triangle be \[3x-2y+6=0\] and \[4x+5y-20=0\] the orthocentre of this triangle is at (1, 1), then the equation of its third side is:

A) \[122y-26x-1675=0\]

B) \[26x+61y+1675=0\]

C) \[122y+26x+1675=0\]

D) \[26x-122y-1675=0\]

Correct Answer: D

Solution :

Equation of AB is \[3x-2y+6=0\]

Equation of AC is \[4x+5y-20=0\]

Equation of BE is \[2x+3y-5=0\]

Equation of CF is \[5x-4y-1=0\]

\[\Rightarrow \] Equation of BC is \[26x-122y=1675.\]