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The points A(k+1, 2x),B(3k, 2k+3),C(5k−1,5k)  are collinear. Value of k for that is ____.


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Detailed Solution

Points that are on the same line are referred to as collinear points. On a line connecting two locations, or more, they can be close together or far apart.
Points A(k+1,2k), B(3k,2k+3) and C(3k−1,5k) are collinear. Therefore, the area of the triangle is 0.
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