1.

Show that the three points (3,0),(-2,-2) and (8,2) are collinear. Also, find the equation of the straight line on which these points lie.

Answer» Let A(3,0),B(-2,-2) and C(8,2) be the given points.
Then, the equation of line AB is given by
`(y-0)/(x-3)=(-2-0)/(-2-3)" "["using"(y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1))]`
`Rightarrow (y)/(x-3)=(2)/(5)........(i)`
`Rightarrow 2x-5y-6=0,` which is the required equation.
Putting x=8 and y=2 in (i), we get
`LHS=(2xx8)-(5xx2)-6=0=RHS`
Thus, the point C(8,2) also lies on (i).
Hence, the given points lie on the same striaght line, whose equation is 2x-5y-6=0.


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