Find the values of x for which the points (x,-1),(2,1) and (4,5)are collinear.

Q.No. 8 of Exercise 10.1 of 11th class
Find the values of x for which the points (x,-1),(2,1) and (4,5)are collinear.


Sol :

            We have the points A(x,-1), B(2,1) and C(4,5).      [Let]
A, B, C are collinear if the slope of AB = slope of BC.


Now

          Slope of AB = 1-(-1)/2-x = 2/2-x
         Slope of BC = 5-1/4-2 = 4/2 = 2

Therefore            2/2-x = 2
                    or     4-2x = 2
                    or     2x    = 2 
Therefore               x  = 1