Question

The orthocentre of the triangle formed by the lines $x + y = 1,2x + 3y = 6$ and $4x - y + 4 = 0$ lies in quadrant.

• A. First
• B. Second
• C. Third
• D. Fourth

Answer 1

Answer: (A)

First

Answer 2

On solving the equations, we get the two vertices

(–3, 4) and $\left( \frac { - 3 } { 7 } , \frac { 16 } { 7 } \right)$. Also perpendicular passes through vertices are $x + 4 y = 13$ and $7 x - 7 y = - 19$. Solving these lines, we get the orthocentre $\left( \frac { 3 } { 7 } , \frac { 22 } { 7 } \right)$ i.e. in first quadrant.