# Show that the following points are collinear. (3, 7), (6, 5) and (15, - 1)

For the points to be collinear the are of the triangle with vertex (3,7),(6,5) and (15,-1) should be zero.

Area of the triangle is given by:

$\\Area = \frac{1}{2}\left [ x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}) \right ] \\(x_1,\ y_1)=(3,\ 7),\ (x_2,\ y_2)=(6,\ 5),\ (x_3,\ y_3)=(15,\ -1) \\Area= \frac{1}{2}\left [ 3(5+1)+6(-1-7)+15(7-5) \right ] \\=0.5[18-48+30]=0$

Therefore the given points are collinear

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