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Question

If the points (2,3),(3,5) and (5,k) are collinear, then the value of k is


Solution

If the points are collinear then the area formed by the three points is 0, so
12x1x2x3x1y1y2y3y1=012235235k3=0|(109)+(3k25)+(152k)|=0|1+3k25+152k|=0k=9

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