Maths / Coordinate Geometry / Area of Triangle Using Coordinate

QUESTION
 

In each of the following find the value of 'k' for which the points are collinear. (8,1), (k,-4), (2,-5)

EXPLANATION
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Text

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

                                              large frac {1}{2}left [ 8(-4+5)+ k(-5-1)+2(1+4) right ]=0

                                            large =frac {1}{2}left [ 8(1)+ k(-6)+2(5) right ]=0

                                            large =frac {1}{2}left [ 8 -6k +10 right ]=0

i.e.,                                          frac {1}{2}(18- 6k)=0

                                              9-3k : =0

Therefore,                              k=3

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