How to solve this 

Asked by Surjitsp6u | 26th Aug, 2019, 11:52: PM

Expert Answer:

 
L e t space B left parenthesis 8 comma space 2 right parenthesis space b e space t h e space r i g h t space a n g l e d space v e r t e x
A B space b e space t h e space p e r p e n d i c u l a r space s i d e space w i t h space e q u a t i o n space x minus 3 y minus 2 equals 0 space.... space left parenthesis i right parenthesis
B C space b e space t h e space b a s e space a n d space A C space t h e space h y p o t e n u s e space w i t h space m i d p o i n t space M left parenthesis 7 comma space 15 right parenthesis
A B perpendicular B C space a n d space B C space p a s s e s space t h r o u g h space B left parenthesis 8 comma space 2 right parenthesis
S l o p e space o f space A B equals 1 third
T h e r e f o r e comma space e q u a t i o n space o f space B C space i s colon
y minus 2 equals negative 3 left parenthesis x minus 8 right parenthesis
rightwards double arrow A B space colon space 3 x plus 2 minus 26 equals 0 space... space left parenthesis i i right parenthesis
S i n c e comma space M space i s space t h e space m i d p o i n t space o f space A C
rightwards double arrow A M equals B M equals C M
B M equals square root of open parentheses 8 minus 7 close parentheses squared plus open parentheses 2 minus 15 close parentheses squared end root equals square root of 170 space... space left parenthesis i i i right parenthesis
L e t space A left parenthesis p comma q right parenthesis space a n d space C left parenthesis a comma b right parenthesis
N o w comma space A B space p a s s e s space t h r o u g h space A rightwards double arrow p minus 3 q minus 2 equals 0 rightwards double arrow p equals 3 q plus 2 space
F r o m space left parenthesis i i i right parenthesis
rightwards double arrow A M equals square root of 170
rightwards double arrow open parentheses p minus 7 close parentheses squared plus open parentheses q minus 15 close parentheses squared equals 170
rightwards double arrow open parentheses 3 q minus 5 close parentheses squared plus open parentheses q minus 15 close parentheses squared equals 170
rightwards double arrow 10 q squared minus 60 q plus 80 equals 0
rightwards double arrow q equals 2 comma space 4 space a n d space p equals 8 comma space 14
rightwards double arrow left parenthesis p comma space q right parenthesis equals left parenthesis 14 comma space 4 right parenthesis space... space left parenthesis i v right parenthesis space sin c e space B space i s space left parenthesis 8 comma space 2 right parenthesis
N o w comma space e q u a t i o n space o f space h y p o t e n u s e space A C space parallel to space A M
E q space o f space A C colon
y minus 4 equals fraction numerator 15 minus 4 over denominator 7 minus 14 end fraction left parenthesis x minus 14 right parenthesis
rightwards double arrow 11 x plus 2 y minus 162 equals 0 space... space left parenthesis v right parenthesis
i n t e r s e c t i o n space o f space B C thin space a n d space A C space i s colon space
C left parenthesis 22 comma space minus 40 right parenthesis space
H e n c e comma space t h e space v e r t i c e s space a r e space A left parenthesis 14 comma space 4 right parenthesis comma space B left parenthesis 8 comma space 2 right parenthesis space a n d space C left parenthesis 22 comma space minus 40 right parenthesis.

Answered by Renu Varma | 27th Aug, 2019, 11:51: AM

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