Sir please solve 

Asked by sanjaysingh.srct | 1st Sep, 2019, 01:02: PM

Expert Answer:

L e t space A B C thin space b e space a space t r i a n g l e
G i v e n colon space B left parenthesis negative 4 comma space minus 5 right parenthesis space a n d space i t space d o e s space n o t space p a s s space t h r o u g h space a n y space o f space t h e space t w o space g i v e n space a l t i t u d e s
T h e space e q u a t i o n s space o f space a l t i t u d e s space a r e colon
A M space t h r o u g h space A colon space 3 x plus 8 y plus 13 equals 0 space.... space left parenthesis i right parenthesis
C N space t h r o u g h space C colon space 5 x plus 3 y minus 4 equals 0 space.... space left parenthesis i i right parenthesis
S l o p e space o f space A B space equals space minus fraction numerator 1 over denominator S l o p e space o f space C N end fraction equals negative fraction numerator 1 over denominator begin display style 5 over 3 end style end fraction equals 3 over 5
S i m i l a r l y comma space s l o p e space o f space B C space equals space minus fraction numerator 1 over denominator S l o p e space o f space A M end fraction equals 8 over 3
E q u a t i o n space o f space A B colon space y equals 3 over 5 x plus c
I t space p a s s e s space t h r o u g h space B rightwards double arrow negative 5 equals negative 12 over 5 plus c rightwards double arrow c equals negative 13 over 5
T h e r e f o r e comma space e q u a t i n space o f space A B space i s space 3 x minus 5 y minus 13 equals 0 space... space left parenthesis i i i right parenthesis
S i m i l a r l y comma space e q u a t i o n space o f space B C thin space i s space 8 x minus 3 y plus 17 equals 0 space..... space left parenthesis i v right parenthesis
A l t i t u d e s space o f space a space t r i a n g l e space i n t e r s e c t space a t space a space p o i n t
I n t e r s e c t i o n space o f space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis space i s space open parentheses 71 over 31 comma space minus 77 over 31 close parentheses
S o comma space a l t i t u d e space t h r o u g h space B space h a s space t h e space s l o p e space equals space fraction numerator negative 5 plus begin display style 77 over 31 end style over denominator negative 4 minus begin display style 71 over 31 end style end fraction equals negative 78 over 195
N o w comma space f i n d space t h e space i n t e r s e c t i o n space o f space A M comma space A B space a n d space C M comma space B C space
T h e n space g e t space t h e space e q u a t i o n space o f space A C.L e t space A B C thin space b e space a space t r i a n g l e
G i v e n colon space B left parenthesis negative 4 comma space minus 5 right parenthesis space a n d space i t space d o e s space n o t space p a s s space t h r o u g h space a n y space o f space t h e space t w o space g i v e n space a l t i t u d e s
T h e space e q u a t i o n s space o f space a l t i t u d e s space a r e colon
A M space t h r o u g h space A colon space 3 x plus 8 y plus 13 equals 0 space.... space left parenthesis i right parenthesis
C N space t h r o u g h space C colon space 5 x plus 3 y minus 4 equals 0 space.... space left parenthesis i i right parenthesis
S l o p e space o f space A B space equals space minus fraction numerator 1 over denominator S l o p e space o f space C N end fraction equals negative fraction numerator 1 over denominator begin display style 5 over 3 end style end fraction equals 3 over 5
S i m i l a r l y comma space s l o p e space o f space B C space equals space minus fraction numerator 1 over denominator S l o p e space o f space A M end fraction equals 8 over 3
E q u a t i o n space o f space A B colon space y equals 3 over 5 x plus c
I t space p a s s e s space t h r o u g h space B rightwards double arrow negative 5 equals negative 12 over 5 plus c rightwards double arrow c equals negative 13 over 5
T h e r e f o r e comma space e q u a t i n space o f space A B space i s space 3 x minus 5 y minus 13 equals 0 space... space left parenthesis i i i right parenthesis
S i m i l a r l y comma space e q u a t i o n space o f space B C thin space i s space 8 x minus 3 y plus 17 equals 0 space..... space left parenthesis i v right parenthesis
A l t i t u d e s space o f space a space t r i a n g l e space i n t e r s e c t space a t space a space p o i n t
I n t e r s e c t i o n space o f space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis space i s space open parentheses 71 over 31 comma space minus 77 over 31 close parentheses
S o comma space a l t i t u d e space t h r o u g h space B space h a s space t h e space s l o p e space equals space fraction numerator negative 5 plus begin display style 77 over 31 end style over denominator negative 4 minus begin display style 71 over 31 end style end fraction equals negative 78 over 195
N o w comma space f i n d space t h e space i n t e r s e c t i o n space o f space A M comma space A B space a n d space C M comma space B C space
T h e n space g e t space t h e space e q u a t i o n space o f space A C.

Answered by Renu Varma | 3rd Sep, 2019, 11:55: AM

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