Question

The three lines 4x-7y+10=0, x+y=5, 7x+4y-15=0 form the sides of a triangle. Then the point (1,2) is

• A. Centroid of the triangle
• B. In-centre of the triangle
• C. Orthocenter of the triangle
• D. Circumcentre of the triangle

Answer 1

The correct option is C

Orthocenter of the triangle

Given sides are 4x-7y+10=0 ........(1)

x+y=5 ........(2)

7x+4y-15=0 ........(3)

Clearly (1) and (3) are perpendicular to each other by solving them we get (1,2)

$\therefore$ (1,2) will be orthocenter of the triangle