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Points A,B, and C lie in a plane. If the distance between A and B is 7 and the distance between B and C is 4 , which of the following could be the distance between A and C.

Asked by sruthi 18th September 2015, 6:18 PM
Answered by Expert
Answer:

Hi Shruthi,

C a s e 1 colon space L e t space t h e space p o i n t s space A comma B space a n d space C space a r e space c o l l i n e a r. S u p p o s e space C space l i e s space b e t w e e n space A space a n d space B. G i v e n 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 equals 7 space u n i t s D i s tan c e space b e t w e e n space B space a n d space C equals space 4 space u n i t s.

T h u s comma space d i s tan c e space b e t w e e n space A space a n d space C equals 7 minus 4 equals 3 space u n i t s.  C a s e 2 colon L e t space t h e space p o i n t s space A comma space B space a n d space C space a r e space c o l l i n e a r. S u p p o s e space C space l i e s space t o space t h e space r i g h t space o f space B.

T h u s space d i s tan c e space b e t w e e n space A space a n d space C equals d i s tan c e space b e t w e e n space A space a n d space B plus d i s tan c e space b e t w e e n space B space a n d space C space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 7 space u n i t s space plus space 4 space u n i t s space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 11 space u n i t s  C a s e 3 colon L e t space t h e space p o i n t s space A comma space B space a n d space C space a r e space n o t space c o l l i n e a r. T h u s comma space t h e space p o i n t s space A comma space B space a n d space C space f o r m space a space t r i a n g l e. B y space t h e space p r o p e r t i e s space o f space a space t r i a n g l e comma space t h e space s u m space o f space a n y space t w o space s i d e s space o f space t h e space t r i a n g l e comma space s h o u l d space b e space g r e a t e r t h a n space t h e space t h i r d space s i d e.

S i n c e space A B equals 7 space u n i t s comma space B C equals 4 space u n i t s comma space C A space s h o u l d space b e space l e s s space t h a n space 7 plus 4 equals 11  S i m i l a r l y comma space C A space s h o u l d space b e space g r e a t e r space t h a n space 3 space b e c a u s e space 4 plus 3 equals 7 T h e r e f o r e comma space 3 less than C A less than 11

Answered by Expert 21st September 2015, 2:03 PM
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