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XAT 2023 — QA & DI Question 2

TrianglesEasy

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:

Answer & solution

  • A

    6abc

  • B

    9abc

  • C

    6bc

  • 9ac

  • E

    None of the above

Solution

​​​​​​​

The length of AC = (b + 4c) - (b - 2c) = 6c

Altitude from C to AB = a - (-2a) = 3a

∴ Area of ABC = 1/2 × b × h = 1/2 × 3a × 6c = 9ac

Hence, option (d).

XAT 2023 QA & DI Q2: ABC is a triangle and the coordinates of A, B and C are (a, b - 2c), (a, b + 4c) and (-2a, 3c) respectively wh — Solution | TheCATExam