If the area of the triangle formed by vertices (-k, k) , (1, 0) , and (5, 0) is 8 square units, then k can be: - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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If the area of the triangle formed by vertices (- k, k), (1, 0), and (5, 0) is 8 square units, then k can be:

Solution & Step-by-step Explanation

The area of a triangle with vertices (x_{1}, y_{1}), (x_{2}, y_{2}), and (x_{3}, y_{3}) is: Area = \frac{1}{2} ∣ x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) ∣ Substitute the vertices (- k, k), (1, 0), and (5, 0) : 8 = \frac{1}{2} ∣ (- k) (0 - 0) + 1 (0 - k) + 5 (k - 0) ∣ 16 = ∣0 - k + 5 k ∣ 16 = ∣4 k ∣ This gives two possibilities: 4 k = 16 ⟹ k = 4 4 k = - 16 ⟹ k = - 4 So, k can be 4 or - 4 .

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If the area of the triangle formed by vertices (- k, k), (1, 0), and (5, 0) is 8 square units, then k can be:

4

- 4

Both (A) and (B)

None of these

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