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with rectangular axes plot the points o(0,0), a(4,0) and c(0,6). find the cordinates of the fourth point b such that oabc forms a rectangle.

Asked by Sanmit Ratnaparkhi 1st March 2015, 8:35 PM
Answered by Expert
Answer:
L e t space O comma space A space a n d space C space b e space t h e space p o i n t s space s u c h space t h a t space t h e space c o o r d i n a t e s space r e s p e c t i v e l y space a r e O open parentheses 0 comma 0 close parentheses comma space A open parentheses 4 comma 0 close parentheses space a n d space C open parentheses 0 comma 6 close parentheses. W e space n e e d space t o 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 B space g i v e n space t h a t space O A B C space i s space a space r e c tan g l e. W e space k n o w space t h a t space i n space a space r e c tan g l e comma space o p p o s i t e space s i d e s space a r e space e q u a l space a n d space a l l space t h e space a n g l e s space a r e space e q u a l. T h u s comma space O A equals B C space a n d space O C equals A B L e t space u s space f i n d space O A. O A equals square root of open parentheses 4 minus 0 close parentheses squared plus open parentheses 0 minus 0 close parentheses squared end root equals 4 space u n i t s T h u s comma space C B equals 4 space u n i t s. T h e r e f o r e comma space t h e space x space c o o r d i n a t e space o f space B space i s space 4 space u n i i t s. S i n c e space t h e space y minus c o o r d i n a t e s space o f space O space a n d space A space a r e space 0 comma space O A space l i e s space o n space t h e space l i n e comma space y equals 0 comma space w h i c h space i s space x space a x i s. L e t space u s space f i n d space O C. O C equals square root of open parentheses 0 minus 0 close parentheses squared plus open parentheses 0 minus 6 close parentheses squared end root equals 6 space u n i t s T h u s comma space O C equals 6 space u n i t s. S i n c e space t h e space x minus c o o r d i n a t e s space o f space O space a n d space C space a r e space 0 comma space O C space l i e s space o n space t h e space l i n e comma space x equals 0 comma space w h i c h space i s space y space a x i s. T h e r e f o r e comma space t h e space y space c o o r d i n a t e space o f space B space i s space 6 space u n i i t s. T h u s space t h e space c o o r d i n a t e s space o f space B space a r e space B open parentheses 4 comma 6 close parentheses.
Answered by Expert 2nd March 2015, 9:57 AM
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