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
Explain TypeExplanation Content
Text

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

$\dpi{120} \large \frac {1}{2}\left [ 7(1-k)+5(k-(-2))+3((-2)-1) \right ]=0$

$\dpi{120} \large \frac {1}{2}\left [ 7-7k+5k +10 -6-3 \right ]=0$

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

Therefore,                              $\large k=4$

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