Archive
21st of September 2015
Mathematics
Q:

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.

Sruthi Aniyan - CBSE - Class IX

Friday, September 18, 2015 at 18:18:PM

A:

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

Monday, September 21, 2015 at 14:03:PM