Question:
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:
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:
Updated On: Aug 9, 2024
- 6abc
- 9abc
- 6bc
- 9ac
- None of the above
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The Correct Option is D
Solution and Explanation
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.
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