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Asked by sanjaysingh.srct | 29 Aug, 2019, 08:18: AM
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L e t space A left parenthesis a comma b right parenthesis comma space B left parenthesis c comma d right parenthesis space a n d space C left parenthesis e comma f right parenthesis space b e space t h e space v e r t i c e s space o f space a space t r i a n g l e x plus y equals 2 space b e space t h e space e q u a t i o n space o f space t h e space s i d e space B C rightwards double arrow c plus d equals 2 space a n d space e plus f equals 2 space... space left parenthesis i right parenthesis C e n t r o i d equals open parentheses fraction numerator a plus c plus e over denominator 3 end fraction comma fraction numerator b plus d plus f over denominator 3 end fraction close parentheses equals open parentheses 0 comma 0 close parentheses rightwards double arrow a plus c plus e equals 0 space a n d space b plus d plus f equals 0 A B C thin space i s space a n space e q u i l a t e r a l space t r i a n g l e rightwards double arrow A B equals B C equals A C T a k i n g space A B equals A C rightwards double arrow open parentheses a minus c close parentheses squared plus open parentheses b minus d close parentheses squared equals open parentheses a minus e close parentheses squared plus open parentheses b minus f close parentheses squared rightwards double arrow c squared minus 2 a c plus d squared minus 2 b d equals e squared minus 2 a e plus f squared minus 2 b f rightwards double arrow c squared minus e squared plus d squared minus f squared minus 2 a c plus 2 a e minus 2 b d plus 2 b f equals 0 rightwards double arrow left parenthesis c minus e right parenthesis left parenthesis c plus e right parenthesis plus left parenthesis d minus f right parenthesis left parenthesis d plus f right parenthesis minus 2 a left parenthesis c minus e right parenthesis minus 2 b left parenthesis d minus f right parenthesis equals 0 rightwards double arrow left parenthesis c minus e right parenthesis open square brackets c plus e minus 2 a close square brackets plus left parenthesis d minus f right parenthesis open square brackets d plus f minus 2 b close square brackets equals 0 F r o m space left parenthesis i right parenthesis space c minus e equals negative left parenthesis d minus f right parenthesis rightwards double arrow negative left parenthesis d minus f right parenthesis open square brackets c plus e minus 2 a close square brackets plus left parenthesis d minus f right parenthesis open square brackets d plus f minus 2 b close square brackets equals 0 rightwards double arrow c plus e minus 2 a equals d plus f minus 2 b rightwards double arrow 2 left parenthesis a minus b right parenthesis equals c plus e minus left parenthesis d plus f right parenthesis F r o m space left parenthesis i i right parenthesis comma space c plus e equals negative a space a n d space d plus f equals negative b rightwards double arrow 2 left parenthesis a minus b right parenthesis equals negative a plus b rightwards double arrow 3 a minus 3 b equals 0 rightwards double arrow a equals b space.... space left parenthesis i i i right parenthesis F r o m space left parenthesis i i right parenthesis rightwards double arrow a plus c plus e equals 0 space a n d space a plus d plus f equals 0 rightwards double arrow c plus e equals d plus f space a n d space f r o m space left parenthesis i right parenthesis space w e space h a v e space c minus e equals negative d plus f F u r t h e r space s o l v i n g space w e space g e t a equals negative 2 equals b comma space c equals 0 comma space d equals 2 comma space e equals 2 space a n d space f equals S o comma space t h e space e q u a t i o n s space o f space o t h e r space t w o space s i d e s space a r e colon 2 x minus y plus 2 equals 0 space a n d space x minus 2 y equals 2
Answered by Renu Varma | 29 Aug, 2019, 11:31: AM

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