Coordinates Actual Question in XAT 2023

Q. ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers. The area of the triangle ABC is:

1. 6abc
2. 9abc
3. 6bc
4. 9ac
5. None of the above

EXPLANATION

D

The length of AB = (b + 4c) - (b - 2c) = 6a (X-coordinates of A&B are same).

The altitude of triangle ABC, CD = a-(-2a)=3a.