First slide

Cartesian plane

Question

The equations to the sides of a triangle are $x - 3 y = 0, 4 x + 3 y = 5$ and $3 x + y = 0$ . The line $3 x - 4 y = 0$ passes through the

Moderate

A

incentre
B

centroid
C

circumcentre
D

orthocentre of the triangle

Solution

Two sides $x - 3 y = 0$ and $3 x + y = 0$ of the triangle being perpendicular to each other, the triangle is right angled at the origin, the point of intersection of these sides. So that origin is the orthocentre of the triangle and the line $3 x - 4 y = 0$ passes through this orthocentre.

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