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Question
Points A(3, 1), B(12, –2) and C(0, 2) cannot be the vertices of a triangle.
Options
True
False
Solution
This statement is True.
Explanation:
Coordinates of A = (x1, y1) = (3, 1)
Coordinates of B = (x2, y2) = (12, – 2)
Coordinates of C = (x3, y3) = (0, 2)
Area of ∆ABC = ∆ = `1/2[x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2)]`
Δ = `1/2 [3 - (2 - 2) + 12(2 - 1) + 0{1 - (- 2)}]`
Δ = `1/2 [3(- 4) + 12(1) + 0]`
Δ = `1/2 (- 12 + 12)` = 0
Area of ΔABC = 0
Since, the points A(3, 1), B(12, – 2) and C(0, 2) are collinear.
Therefore, the points A(3, 1), B(12, – 2) and C(0, 2) can’t be the vertices of a triangle.
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