What do we learn from Distance and Section Formula and also why do we use it.I also Did not understand some parts of the chapter.

Asked by hvasisht16 | 27th Apr, 2016, 05:21: PM

Expert Answer:

L e t space P left parenthesis x subscript 1 comma y subscript 1 right parenthesis space a n d space Q open parentheses x subscript 2 comma y subscript 2 close parentheses space b e space t w o space p o i n t s.
D i s tan c e space b e t w e e n space P space a n d space Q space i s space g i v e n space b y space d i s tan c e space f o r m u l a comma
d equals square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root

S e c t i o n space f o r m u l a space i s space u s e d space w h e n space a space p o i n t space d i v i d e s space a space l i n e space i n space a space p a r t i c u l a r space r a t i o comma space m colon n
L e t space A space b e space t h e space p o i n t space A open parentheses x subscript 1 comma y subscript 1 close parentheses space a n d space B space b e space t h e space p o i n t space B open parentheses x subscript 2 comma y subscript 2 close parentheses
L e t space P open parentheses x comma y close parentheses space b e space a n y space p o i n t space o n space t h e space l i n e space A B
T h u s comma space
x equals fraction numerator m x subscript 2 plus n x subscript 1 over denominator m plus n end fraction space a n d space y equals fraction numerator m y subscript 2 plus n y subscript 1 over denominator m plus n end fraction

A p p l i c a t i o n s space o f space d i s tan c e space f o r m u l a colon
L e t space A open parentheses x subscript 1 comma y subscript 1 close parentheses space a n d space B open parentheses x subscript 2 comma y subscript 2 close parentheses space b e space t w o space c i t i e s space i n space t h e space c o o r d i n a t e space p l a n e space X Y.
T h e space d i s tan c e space b e t w e e n space t h e space t w o space c i t i e s space i n space t h e space c o o r d i n a t e space p l a n e space i s space t h e space r e a l space l i f e space a p p l i c a t i o ln space o f space D i s tan c e space f o r m u l a.

A p p l i c a t i o n s space o f space s e c t i o n space f o r m u l a colon
L e t space A open parentheses x subscript 1 comma y subscript 1 close parentheses space a n d space B open parentheses x subscript 2 comma y subscript 2 close parentheses space b e space t w o space c i t i e s space i n space t h e space c o o r d i n a t e space p l a n e space X Y.
S u p p o s e space a space p e r s o n space i s space g o i n g space f r o m space A space t o space B space t h r o u g h space c a r.
A s s u m e space t h a t space d i s tan c e space b e t w e e n space A space a n d space B space i s space 500 space k m
L e t space u s space a s s u m e space t h a t space a space p e r t r o l space s t a t i o n space i s space t h e r e space a t space 300 space k m space a w a y space f r o m space A space a n d space 200 space k m space a w a y space f r o m space B.
T h e n space w h a t space a r e space c o o r d i n a t e s space o f space t h e space p e t r o l space s t a t i o n space i n space t h e space c o o r d i n a t e space p l a n e.

W e space c a n space f i n d space t h e space c o o r d i n a t e s space o f space t h e space p e t r o l space p u m p i n g space s t a t i o n space t h r o u g h space s e c t i o n space f o r m u l a.

Answered by Vimala | 28th Apr, 2016, 11:07: AM

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