Question

Let the equations of two sides of a triangle be $3x - 2y + 6 = 0$ and $4x + 5y - 20 = 0$. If 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. $26x - 122y - 1675 = 0$

Answer 1

Answer: (D)

$26x - 122y - 1675 = 0$

Answer 2

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 $26x - 122y = 1675$