please solve this

Asked by Latha | 7th Nov, 2017, 06:30: PM

Expert Answer:

begin mathsize 12px style T o space f i n d space e q space o f space l i n e space F C colon
F identical to left parenthesis 0 comma 5 right parenthesis space a n d space C identical to left parenthesis 10 comma 0 right parenthesis
S l o p e space o f space F C equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator 10 minus 5 over denominator 10 minus 0 end fraction equals 5 over 10 equals 1 half
E q space i n space s l o p e minus i n t e r c e p t space f o r m space i s space n o w colon
y equals 1 half x plus c
T o space f i n d space c comma space s u b s t i t u t i n g space t h e space v a l u e space o f space left parenthesis 0 comma 5 right parenthesis comma space w e space g e t colon
5 equals 1 half left parenthesis 0 right parenthesis plus c
therefore c equals 5
E q space o f space l i n e space F C space i s space y equals 1 half x plus 5
E q space i n space s tan d a r d space f o r m space i s space 1 half x minus y equals negative 5... left parenthesis 1 right parenthesis

S i m i l a r l y comma space w e space g e t space t h e space e q u a t i o n space o f space l i n e space B E space a s space 2 x plus y equals 20... left parenthesis 2 right parenthesis

S o l v i n g space e q space 1 space a n d space 2 space s i m u l tan e o u s l y comma space w e space g e t colon
space space space space space space space space 1 half x minus y equals negative 5
left parenthesis plus right parenthesis space space space space 2 x plus y equals 20
_ _ _ _ _ _ _ _ _ _ _ _ _ _
1 half x plus 2 x equals 15
fraction numerator 5 x over denominator 2 end fraction equals 15
x equals 6
2 left parenthesis 6 right parenthesis plus y equals 20
therefore y equals 8
C o o r d i n a t e s space o f space p o i n t space G identical to left parenthesis 6 comma 8 right parenthesis

U sin g space d i s tan c e space f o r m u l a space t o space f i n d space t h e space l e n g h space o f space A G semicolon
d left parenthesis A G right parenthesis equals square root of left parenthesis x subscript 2 minus x subscript 1 right parenthesis squared plus left parenthesis y subscript 2 minus y subscript 1 right parenthesis squared end root
space space space space space space space space space space space equals square root of left parenthesis 6 minus 0 right parenthesis squared plus left parenthesis 8 minus 0 right parenthesis squared end root
space space space space space space space space space space space equals square root of 36 plus 64 end root
space space space space space space space space space space space equals square root of 100
space space space space space space space space space space space equals 10 space u n i t s

therefore T h e space l e n g t h space o f space A G space i s space 10 space u n i t s.


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Answered by Nooren | 11th Dec, 2017, 02:05: PM