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.
 

Answers (1)
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

Exams
Articles
Questions