Question

Prove that (a,0),(0,b) and (1,1) are collinear,if 1/a+1/b=1.

Answer 1

I do in this way....

If A(a,0),B(0,b),C(1,1) are collinear,
Area(triangle ABC)=0

1/2[X1(y2-y3)+X2(y3-y1)+x3(y1-y2)]=0
[a(b-1)+0(1-0)+1(0-b)=0
[ab-a-b]=0
ab=a+b
Dividing throughout by ab we get
1=1/a+1/b
Therefore,1/a+1/b=1
Thus proved.....Is it right???

Answer 2

The line containing (a,0),(0,b) has equation

x/a + y/b = 1

This is called the intercept form of a line.

Clearly, (1,1) lies on that line if 1/a + 1/b = 1

Answer 3

Did you ever heard about google?

Paste your question in google and you will find couple proves.

Answer 4

I like Elsa's proof, using Heron's formula. Works for me.

Answer 5

Thanks Steve..:-))


@Bosnian:- I already told that I have no enough time for wasting.
After posting the question here,I can do the remaining questions in my book.understood:-))

Answer 6

Steve,yesterday I asked a question and u answered that but u r confused and asked me how do u got 25 as answer?did u remember that?and I answered how I got the answer as 25.can u please check it out whether it is right or not?

Forgot to say thank u to Bosnian..:)

Answer 7

I like your 25 stones.

Answer 8

Really..Anyway thanks Steve:)