Question
Quantitative Ability and Data Interpretation Question on Triangles, Circles & Quadrilaterals
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:
A
6abc
B
9abc
C
6bc
D
9ac
E
None of the above
Answer
9ac
Explanation
Solution
Area of the triangle = 1/2 |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
Area of the triangle = 1/2 |a((b+4c)-3c) + a(3c-(b-2c)) + 2a(b-2c)-(b+4c))|
Area of the triangle = 1/2 |a(b+c) + a(5c-b) - 2a(-6c)|
Area of the triangle = 1/2 |ab + ac + 5ac - ab + 12ac| = 1/2 |18ac| = 9ac
Hence, option D is the correct answer.