Question

determine if the points (1,5),(2,3) and (-2,11) are collinear.​

Answer 1

Question :-

determine the points (1,5),(2,3) and (-2,11) are collinear.

Formula used :-

For collinearity of three points ,

$\: \boxed{ 0 = \small \frac{1}{2} \big( \: x_1(y_2 - y_3) + x_2(y_3 - y_1) +x_3(y_1 - y_2) \big)}$

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Solution :-

Given that :-

Given points are ( 1,5) , (2,3) and (-2,11)

$let \\ x_1 = 1 ,\: y_1 = 5 \\ \\ x_2 = 2 \: , \: y_2 = 3 \\ \\ x_3 = - 2 \: , \: y_3 = 11$

Now using the given formula ,

$\small \: 0 = \frac{1}{2} \big(1(3 - 11) + 2(11 - 5) - 2(5 - 3) \big) \\ \\ \implies \: 0 = \frac{1}{2} \big( - 8 + 12 - 4) \\ \\ \implies \: 0 = \frac{1}{2} ( - 12 + 12) \\ \\ \implies \: \boxed{0 = 0}$

Hence proved,

The given points are collinear.

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Answer 2

Answer:

Question :-

determine the points (1,5),(2,3) and (-2,11) are collinear.

Formula used :-

For collinearity of three points ,

$\: \boxed{ 0 = \small \frac{1}{2} \big( \: x_1(y_2 - y_3) + x_2(y_3 - y_1) +x_3(y_1 - y_2) \big)}$

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Solution :-

Given that :-

Given points are ( 1,5) , (2,3) and (-2,11)

$let \\ x_1 = 1 ,\: y_1 = 5 \\ \\ x_2 = 2 \: , \: y_2 = 3 \\ \\ x_3 = - 2 \: , \: y_3 = 11$

Now using the given formula ,

$\small \: 0 = \frac{1}{2} \big(1(3 - 11) + 2(11 - 5) - 2(5 - 3) \big) \\ \\ \implies \: 0 = \frac{1}{2} \big( - 8 + 12 - 4) \\ \\ \implies \: 0 = \frac{1}{2} ( - 12 + 12) \\ \\ \implies \: \boxed{0 = 0}$

Hence proved,

The given points are collinear.

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