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  • By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear.

Q20: By using the concept of equation of a line, prove that the three points  (3,0),(-2,-2) and  (8,2)  are collinear.
 

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Points are collinear, means they lies on same line
Now,  given points are   A(3,0),B(-2,-2) and  C(8,2)
equation of line passing through point A and B is
(y-0)=\frac{0+2}{3+2}(x-3)
y=\frac{2}{5}(x-3)\Rightarrow 5y= 2(x-3)
2x-5y=6
Therefore, the equation of line passing through A and B is 2x-5y=6

Now, Equation of line passing through point B and C is
(y-2)=\frac{2+2}{8+2}(x-8)
(y-2)=\frac{4}{10}(x-8)
(y-2)=\frac{2}{5}(x-8) \Rightarrow 5(y-2)=2(x-8)
5y-10=2x-16
2x-5y=6
Therefore, equation of line passing through point B and C is 2x-5y=6
We can clearly see that  Equation of line passing through point A and B and through B and C is the same.  
By this, we can say that points  A(3,0),B(-2,-2) and  C(8,2) are collinear points

Posted by

Gautam harsolia

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