# Q : 20    By using the concept of equation of a line, prove that the three points  $(3,0),(-2,-2)$ and  $(8,2)$  are collinear.

G Gautam harsolia

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 $2x-5y=6$
When can clearly see that  Equation of line passing through point A nd 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

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