If the points (a,0),(0,b) and (1,1) are collinear ,show that (1/a)+(1/b)=1

find the area of triangle and equate to zero 

Simple,

slope of line passing through (a,0) and (0,b) = (b-0)/(0-a) = -b/a

again, slope of line passing through (0,b) and (1,1) = (1 - b)/1 = (1 - b)

Now, since (a,0),(0,b) and (1,1) are collinear thus,

-b/a = 1 - b

=> -b = a - ab

=> a + b = ab

on dividing both sides by ab we get,

1/a + 1/b = 1 proved...............!!

If these points are co-linear then the area of triangle = 0

so, area of triangle 1/2(ab + 0+ 0-{0+b+a} )=0

  or  ab-(a+b)=0 

  or ab = a+b  -(i)

 Since  (1/a)+(1/b)= (a+b)/ab

 or ab/ab =1 { a+b = ab }