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Question
The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.
Options
True
False
Solution
This statement is False.
Explanation:
Given points are A(– 2, 1), B(0, 5), C(– 1, 2)
Area of ΔABC = `1/2|(-2, 1, 1),(0, 5, 1),(-1, 2, 1)|`
= `1/2 -2|(5, 1),(2, 1)| -1|(0, 1),(-1, 1)| + 1|(0, 5),(-1, 2)|`
= `1/2 |-2(5 - 2) - 1(0 + 1) + 1(0 + 5)|`
= `1/2 |-2 xx 3 - 1 xx 1 + 1 xx 5|`
= `1/2|-6 - 1 + 5|`
= `1/2|-2|`
= 1 sq.unit
So, the given points are not collinear.
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