Can You Plz Explain Me These Formulas?

Asked by venkat34 | 17th Dec, 2015, 09:01: PM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
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 p o i n t s space a n d space A B space b e space t h e space l i n e space j o i n i n g space t h e space t w o space p o i n t s. L e t space P open parentheses x comma y close parentheses space b e space a space p o i n t space w h i c h space d i v i d e s space t h e space l i n e space A B space i n space t h e space r a t i o space m colon n T h e n 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 o i n t space P space a r e colon open parentheses fraction numerator m x subscript 2 plus n x subscript 1 over denominator m plus n end fraction comma fraction numerator m y subscript 2 plus n y subscript 1 over denominator m plus n end fraction close parentheses  T h e r e f o r e comma space i f space t h e space n u m b e r s space m space a n d space n space a r e space p o s i t i v e space i n t e g e r s space o r space i f space t h e space r a t i o space i s space m colon n comma space t h e n space w e space c a n space u s e space t h e space s e c t i o n space f o r m u l a. space open parentheses fraction numerator m x subscript 2 plus n x subscript 1 over denominator m plus n end fraction comma fraction numerator m y subscript 2 plus n y subscript 1 over denominator m plus n end fraction close parentheses  E x a m p l e colon space I f space A open parentheses negative 2 comma 3 close parentheses space a n d space B open parentheses 2 comma 0 close parentheses space a r e space t w o space p o i n t s space o f space t h e space l i n e space j o i n i n g space A a n d space B comma space a n d space i f space P open parentheses x comma y close parentheses space i s space a n y space p o i n t space i n b e t w e e n space A B comma space s u c h space t h a t space P space d i v i d e s space A B space i n space t h e space r a t i o space 2 colon 3 comma space t h e n space t h e space c o o r d i n a t e s space o f space P space a r e space g i v e n space b y space t h e space f o r m u l a space space open parentheses fraction numerator m x subscript 2 plus n x subscript 1 over denominator m plus n end fraction comma fraction numerator m y subscript 2 plus n y subscript 1 over denominator m plus n end fraction close parentheses   N o w space i f space t h e space n u m b e r space apostrophe k apostrophe space i s space a space p o s i t i v e space r a t i o n a l space n u m b e r comma space t h a t space i s space k equals m over n comma space o r space i f space t h e space r a t i o space i s space k colon 1 t h e n space w e space c a n space u s e space t h e space s e c t i o n space f o r m u l a comma space open parentheses fraction numerator k x subscript 2 plus x subscript 1 over denominator m plus n end fraction comma fraction numerator k y subscript 2 plus y subscript 1 over denominator m plus n end fraction close parentheses E x a m p l e colon space I f space A open parentheses negative 2 comma 3 close parentheses space a n d space B open parentheses 2 comma 0 close parentheses space a r e space t w o space p o i n t s space o f space t h e space l i n e space j o i n i n g space A a n d space B comma space a n d space i f space P open parentheses x comma y close parentheses space i s space a n y space p o i n t space i n b e t w e e n space A B comma space s u c h space t h a t space P space d i v i d e s space A B space i n space t h e space r a t i o space 2 over 3 colon 1 comma space t h e n space t h e space c o o r d i n a t e s space o f space P space a r e space g i v e n space b y space t h e space f o r m u l a space open parentheses fraction numerator k x subscript 2 plus x subscript 1 over denominator m plus n end fraction comma fraction numerator k y subscript 2 plus y subscript 1 over denominator m plus n end fraction close parentheses

Answered by Vimala Ramamurthy | 18th Dec, 2015, 10:46: AM