Question

prove that the points 2, 3, - 4, _6 and 1, 3/2 do not form a triangle​

Answer 1

It is known that three points (x1, y1), (x2, y2) and (x3, y3) do not form a triangle, if they are collinear.

It is possible if

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Answer 2

The points (2,3),(-4,-6),(1,$\frac{3}{2}$) do not form triangle.

Step-by-step explanation:

Given points are (2,3),(-4,-6),(1,$\frac{3}{2}$)

We have to prove that,the given points do not form triangle.

⇒The given points are collinear.

Let$(x_1,y_2),(x_2,y_2),(x_3,y_3)$ are the points.

$\bold {Area\ of\ triangle = \frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}]$

For collinear points Area of triangle = 0

Area of triangle =$\frac{1}{2}[2(-6-\frac{3}{2})+(-4)(\frac{3}{2}-3)+1(3-(-6)]$

                          = $\frac{1}{2} [-15+6+9]$

                          = 0

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