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Asked by araima2001 | 4th Dec, 2016, 05:12: PM

Expert Answer:

 
begin mathsize 16px style The space given space lines space are space straight a space family space of space lines space that space pass space through space the space intersection space of space the space following space two space lines colon
straight x minus 2 straight y plus 3 equals 0 space and space 2 straight x minus 3 straight y plus 4 space equals space 0
On space solving space the space two space equations comma space we space can space obtain space the space intersection
Let space the space intersection space of space the space space lines space be space straight J space equals space left parenthesis 1 comma 2 right parenthesis
Let space straight P space equals space left parenthesis straight a comma straight b right parenthesis space be space the space image space of space the space point space straight Q equals left parenthesis 2 comma 3 right parenthesis
Then space the space mid minus point space straight M space equals space open parentheses fraction numerator straight a plus 2 over denominator 2 end fraction comma fraction numerator straight b plus 3 over denominator 2 end fraction close parentheses space of space PQ.
In space the space given space figure comma space consider space increment JMQand space increment JMP comma
JM space equals space JM space left parenthesis common space side right parenthesis
angle JMQ equals angle JMP space left parenthesis each space is space 90 degree right parenthesis
QM space equals MP space left parenthesis straight M space is space the space mid minus point space of space PQ right parenthesis
rightwards double arrow increment JMQ approximately equal to increment JMP space space space left parenthesis SAS space congruence space criterion right parenthesis
rightwards double arrow JQ equals JP
rightwards double arrow left parenthesis 2 minus 1 right parenthesis squared plus left parenthesis 3 minus 2 right parenthesis squared equals left parenthesis straight a minus 1 right parenthesis squared plus left parenthesis straight b minus 2 right parenthesis squared
rightwards double arrow 2 equals left parenthesis straight a minus 1 right parenthesis squared plus left parenthesis straight b minus 2 right parenthesis squared
rightwards double arrow 2 equals straight a squared minus 2 straight a plus 1 plus straight b squared minus 4 straight b plus 4
rightwards double arrow straight a squared minus 2 straight a plus straight b squared minus 4 straight b plus 3 equals 0
Replacing space straight a space by space straight x space and space straight b space by space straight y space we space get comma
rightwards double arrow straight x squared minus 2 straight x plus straight y squared minus 4 straight y plus 3 equals 0
Hence space the space correct space option space is space left parenthesis straight c right parenthesis. end style

Answered by Rebecca Fernandes | 6th Dec, 2016, 09:58: AM