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

Asked by niharika | 27th Jan, 2016, 06:28: PM

Expert Answer:

 

Slope space of space line space joining space left parenthesis straight a comma space 0 right parenthesis space and space left parenthesis 0 comma space straight b right parenthesis equals fraction numerator straight b minus 0 over denominator 0 minus straight a end fraction equals negative straight b over straight a Slope space of space the space line space joining space left parenthesis straight a comma space 0 right parenthesis space and space left parenthesis 1 comma space 1 right parenthesis equals fraction numerator 1 minus 0 over denominator 1 minus straight a end fraction equals fraction numerator 1 over denominator 1 minus straight a end fraction If space the space three space points space are space collinear comma space minus straight b over straight a equals fraction numerator 1 over denominator 1 minus straight a end fraction rightwards double arrow negative straight b plus ab equals straight a Diving space both space sides space by space apostrophe ab apostrophe space we space get minus 1 over straight a plus 1 equals 1 over straight b rightwards double arrow 1 over straight a plus 1 over straight b equals 1 left parenthesis Proved right parenthesis

Answered by  | 27th Jan, 2016, 06:38: PM

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