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Question

# The points (k,3),(2,−4) and (−k+1,−2) are collinear, find k.

A
13
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B
3
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C
1
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D
3
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Solution

## The correct option is A −13When three points A, B and C arecollinear, slope of line joining any two points (say AB) = slope of linejoining any other two points (say BC). Slope of the line passing through points (x1,y1) and (x2,y2) = y2−y1x2−x1Slope of the line passing through (k,3) and (2,−4)=Slope of line passing through ((−k+1),−2) and (2,−4) −4−32−k=−4−(−2)2−(−k+1)−72−k=−21+kOn cross multiplying and solving, we get k =−13

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