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Question
The points (0, 5), (0, –9) and (3, 6) are collinear.
Options
True
False
Solution
This statement is False.
Explanation:
The points are collinear if area of a triangle formed by its points is equals to the zero.
Given,
x1 = 0, x2 = 0, x3 = 3 and y1 = 5, y2 = – 9, y3 = 6
∵ Area of triangle = `1/2[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]`
Δ = `1/2[0(-9 - 6) + 0(6 - 5) + 4(5 + 9)]`
Δ = `1/2(0 + 0 + 3 xx 14)`
Δ = `42/2 = 21 ≠ 0`
From the above equation, it is clear that the points are not collinear.
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