If three points (h.0),(a,b) and (0,k) lie on line, show that a/h+b/k=1

Q.No. 13 of Exercise 10.1 of Class 11th

If three points (h.0),(a,b) and (0,k) lie on line, show that a/h+b/k=1.

Sol :
Let, 
   The given points are A(h,0), B(a,b), C(0,k)
   These points lie on the same line

Therefore,  
      Slope of AB = Slope of BC.


Here, 
Slope of AB = b-0/a-h = b/a-h

Slope of BC = k-b/0-a = k-b/-a


Now

              b/a-h = k-b/-a
Or            -ab = (a-h)(k-b)               [By Cross Multiplication]
Or            -ab = ak-ab-hk+bh
Or               0 = ak-hk+bh
Or     ak+bh  = hk

Dividing both side by hk, we get
            
                        ak/hk + bh/hk = hk/hk
Or                   a/h + b/k = 1