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

Asked by toppin | 28th Sep, 2010, 05:34: PM

Expert Answer:

lets call them A,B,C respectively.
since they lie on the same line, so
slope of AB=slope of BC=slope of AC
slope of AB=b-0/a-h..(i)
slope of BC=k-b/0-a..(ii)
slope of AC=k-0/0-h..(iii)
from (i) and (iii0 we get
b/a-h=k/-h
so
b(-h)=k(a-h)
i e.
-bh=ak-kh
i.e.
ak+bh=kh
dividing by kh both sides,
a/h  +b/k  =1
 hence the answer.

Answered by  | 28th Sep, 2010, 06:05: PM

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