Question

prove that the points (-1,-1),( 2,3), (8,11) are collinear
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Answer 1

Answer:

I found the answer for your question.

Step-by-step explanation:

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Answer 2

Answer:

$\bf \large\underbrace\orange{Question:}$

• Prove that the points (-1,-1), ( 2,3), (8,11) are collinear.

$\bf\underbrace\orange{Answer:}$

$\bf\underbrace\orange{Concept \: used:}$

There are 4 methods to show that 3 points are collinear :-

• 1. Using Distance Formula
• 2. Using Section Formula
• 3. Area of triangle is 0.
• 4. Slope Method.

So, here slope method is used in this solution.

Method :-

• Find the slope of AB.
• Find the slope of BC.
• If, slope of AB = slope of BC
• ⇛ AB || BC
• ⇛ Points A, B, C are collinear.

$\bf\underbrace\orange{Identity \: Used :}$

$\bf \:Let \: the \: coordinates \: be \: A(x_1,y_1) \: and \: B(x_2,y_2)$

$\bf \:Slope \: of \: AB = \dfrac{y_2-y_1}{x_2-x_1}$

$\bf\underbrace\orange{Solution:}$

Let the coordinates be A(-1,-1), B( 2,3), C(8,11)

$\bf \:Slope \: of \: AB = \dfrac{3 - ( - 1)}{2 - ( - 1)} = \dfrac{4}{3}$

$\bf \:Slope \: of \: BC = \dfrac{11 - 3}{8 - 2} = \dfrac{8}{6} = \dfrac{4}{3}$

$\bf\implies \:slope \: of \: AB = slope \: of \: BC$

$\bf\implies \:AB || BC$

$\bf\implies \:Points \: A, B, C \: are \: collinear.$

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