Line q is defined by the equation y = mx + b, where m < 0. Does line q pass through (5,4)?
(1) When it is reflected around the x-axis, line q passes through (3,-4)
(2) When it is reflected around the y-axis, line q passes through (-5,3)
coodinate
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- manpsingh87
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1) line y=mx+b; after reflection around x-axis passes through (3,-4), therefore line must pass through the point (3,4); now if (5,4) also passes through the line than slope would be zero,which will violate the initial condition of m<0; therefore (5,4) won't pass through the line y=mx+b; hence is sufficientcuty wrote:Line q is defined by the equation y = mx + b, where m < 0. Does line q pass through (5,4)?
(1) When it is reflected around the x-axis, line q passes through (3,-4)
(2) When it is reflected around the y-axis, line q passes through (-5,3)
2) line y=mx+b; after reflection around y-axis passes through(-5,3), therefore line must pass through the point (5,3),similarly if(5,4) passes through the line than slope would be zero,therefore (5,4) won't pass through the line y=mx+b; hence is sufficient..!!
hence D
Last edited by manpsingh87 on Sun Apr 17, 2011 9:30 am, edited 1 time in total.
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- force5
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good question again cuty.
here is what i think
statement 1 says - line passes through ( 3,4), since refection passes through (3,-4)
now this means line has negative slope and passes through (3,4). now see that the point (5,4) is parallel to this point on Y axis. which means that if the line passes through both points its slope will be zero. hence it cant pass. (sufficient)
Statement 2- says it passes through (5,3) .. same reasoning as above.
now this means the point (5,4) will be again parallel to the point (5,3) ( this time vertically.)
if the line were to pass through both points its slope cannot be determined.
We again get the answer( hence sufficient)
Hence answer is D
Sorry i didnt know how to draw a graph and attach or else i would have.
Hope it helps. let me know if anyone needs any further explanation
here is what i think
statement 1 says - line passes through ( 3,4), since refection passes through (3,-4)
now this means line has negative slope and passes through (3,4). now see that the point (5,4) is parallel to this point on Y axis. which means that if the line passes through both points its slope will be zero. hence it cant pass. (sufficient)
Statement 2- says it passes through (5,3) .. same reasoning as above.
now this means the point (5,4) will be again parallel to the point (5,3) ( this time vertically.)
if the line were to pass through both points its slope cannot be determined.
We again get the answer( hence sufficient)
Hence answer is D
Sorry i didnt know how to draw a graph and attach or else i would have.
Hope it helps. let me know if anyone needs any further explanation
- manpsingh87
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agreed, i should have checked the conditions properly before jumping on to the conclusion, damn i'm keep on repeating silly mistakes again and again...!!!force5 wrote:good question again cuty.
here is what i think
statement 1 says - line passes through ( 3,4), since refection passes through (3,-4)
now this means line has negative slope and passes through (3,4). now see that the point (5,4) is parallel to this point on Y axis. which means that if the line passes through both points its slope will be zero. hence it cant pass. (sufficient)
Statement 2- says it passes through (5,3) .. same reasoning as above.
now this means the point (5,4) will be again parallel to the point (5,3) ( this time vertically.)
if the line were to pass through both points its slope cannot be determined.
We again get the answer( hence sufficient)
Hence answer is D
Sorry i didnt know how to draw a graph and attach or else i would have.
Hope it helps. let me know if anyone needs any further explanation
and i'm editing my previous post...!!!
O Excellence... my search for you is on... you can be far.. but not beyond my reach!