Maths / Coordinate Geometry / Area of Triangle Using Coordinate

QUESTION
 

Find the value of 'k' for which the points are collinear. (7,-2), (5,1), (3,k).

EXPLANATION
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Since the given points are collinear, the area of the triangle formed by them must be 0,i.e.,

                                             large frac {1}{2}left [ 7(1-k)+5(k-(-2))+3((-2)-1) right ]=0

                                             large frac {1}{2}left [ 7-7k+5k +10 -6-3 right ]=0

i.e.,                                         large frac {1}{2}(-2k + 8)=0

Therefore,                              large k=4

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