Question

prove that (2,-3) (-6,9) (-2,3) are collinear​

Answer 1

Answer:

it can be by representing the points on graph.

Step-by-step explanation:

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Answer 2

Solution :-

Let :-

The points be A ( 2 , -3 ), B ( -6 , 9 ) and C ( -2 , 3 ).

The given points are said to be collinear if area of triangle ABC is equal to zero.

$\boxed{\bf Area \ of \ triangle = \dfrac{1}{2} \times [ \ x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}$

Here :-

$\bullet \sf \ x_1 = 2 \ , \ y_1 = -3 \\\\\bullet \ x_2 = -6 \ , \ y_2 = 9 \\\\\bullet \ x_3 = -2 \ , \ y_3 = 3$

$\longrightarrow \sf \dfrac{1}{2} \times [ \ 2(9-3)+-6(3-(-3))+-2(-3-9) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ 2 (9-3)+-6(3+3)+-2(-3-9) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ ( 2 \times 6)+(-6 \times 6)+(-2 \times -12 ) \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ 12-36+24 \ ] \\\\\longrightarrow \dfrac{1}{2} \times [ \ -24+24 \ ] \\\\\longrightarrow \dfrac{1}{2} \times 0\\\\\longrightarrow 0$

∴ The given points are collinear.