Question

Prove that the points (2,3) , (-4,-6) and (1,$\frac{3}{2} )$ do not form a triangle.

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Answer 1

Let the three points be A(2,3), B(-4,-6), C(1, 3/2).

Let the slope of line AB be a, BC b, CA c.

$a=\frac{3+6}{2+4} =\frac{9}{6} =\frac{3}{2}$

$b=\frac{-6-\frac{3}{2} }{-4-1}=\frac{\frac{15}{2} }{5} =\frac{3}{2}$

$c=\frac{\frac{3}{2} -3}{1-2} =\frac{\frac{3}{2} }{1} =\frac{3}{2}$

If three lines have same slope, they are parallel or coincidental.

And such lines don't form a triangle.

Hence, the points don't form a triangle.

Proved

Answer 2

Answer:

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