please kindly explain the solution of the Q.......

Asked by araima2001 | 31st Jul, 2016, 07:00: PM

Expert Answer:

Length space of space the space line space segment space joining space straight A left parenthesis 6 comma space 3 right parenthesis space space and space straight B left parenthesis negative 1 comma space minus 4 right parenthesis space is space given space by comma
equals square root of open parentheses negative 1 minus 6 close parentheses squared plus open parentheses negative 4 minus 3 close parentheses squared end root
equals square root of 49 plus 49 end root
equals 7 square root of 2 space units

Length space space of space line space segment space AB space is space doubled space by space having space its space length space added space to space each space end.
That space means space length space space of space line space segment space AB space is space doubled space by space adding space 3.5 square root of 2 space units space to space each space end.

Let space straight A apostrophe left parenthesis straight x subscript 1 comma space straight y subscript 1 right parenthesis space and space straight B apostrophe left parenthesis straight x subscript 2 comma space straight y subscript 2 right parenthesis space be space the space cooedinates space of space the space new space ends.

Now space length space of space segment space AA apostrophe space is space 3.5 square root of 2 space units.
rightwards double arrow square root of open parentheses straight x subscript 1 minus 6 close parentheses squared plus open parentheses straight y subscript 1 minus 3 close parentheses squared end root equals space 3.5 square root of 2
rightwards double arrow open parentheses straight x subscript 1 minus 6 close parentheses squared plus open parentheses straight y subscript 1 minus 3 close parentheses squared space equals space 24.50
rightwards double arrow straight x subscript 1 squared minus 12 straight x subscript 1 plus 36 plus straight y subscript 1 squared minus 6 straight y subscript 1 plus 9 space equals space 24.50
rightwards double arrow straight x subscript 1 squared minus 12 straight x subscript 1 plus straight y subscript 1 squared minus 6 straight y subscript 1 space equals space minus 20.50....... left parenthesis straight i right parenthesis

Length space space of space segment space BA apostrophe space is space left parenthesis 3.5 square root of 2 plus 7 square root of 2 right parenthesis space units
rightwards double arrow square root of open parentheses straight x subscript 1 plus 1 close parentheses squared plus open parentheses straight y subscript 1 plus 4 close parentheses squared end root equals space 10.5 square root of 2
rightwards double arrow open parentheses straight x subscript 1 plus 1 close parentheses squared plus open parentheses straight y subscript 1 plus 4 close parentheses squared space equals space 220.50
rightwards double arrow straight x subscript 1 squared plus 2 straight x subscript 1 plus 2 plus straight y subscript 1 squared plus 8 straight y subscript 1 plus 16 space equals space 220.50
rightwards double arrow straight x subscript 1 squared plus 2 straight x subscript 1 plus straight y subscript 1 squared plus 8 straight y subscript 1 space equals space 202.50....... left parenthesis ii right parenthesis

Solving space equation space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space simultaneously space we space get
straight x subscript 1 space equals space 9.5 space space space space and space space space space straight y subscript 1 space equals space 6.5


Simillarly space form space equation space for space straight x subscript 2 space and space space straight y subscript 2 space using space length space of space the space segments space straight B apostrophe straight B space and space straight B apostrophe straight A.
Solving space them space we space get comma
straight x subscript 2 space equals space minus 4.5 space space space space and space space space space straight y subscript 1 space equals space minus 7.5


So space coordinates space of space new space ends space are space left parenthesis 9.5 comma space 6.5 right parenthesis space space space and space space left parenthesis negative 4.5 comma space minus 7.5 right parenthesis.

Answered by Vijaykumar Wani | 1st Aug, 2016, 12:47: PM

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