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by cuty » Sun Apr 17, 2011 5:50 am
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)
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by manpsingh87 » Sun Apr 17, 2011 7:47 am
cuty 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)
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 sufficient

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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by force5 » Sun Apr 17, 2011 8:28 am
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
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by manpsingh87 » Sun Apr 17, 2011 9:11 am
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
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...!!! :evil: :evil:
and i'm editing my previous post...!!!
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by havok » Sun Apr 17, 2011 1:06 pm
Wow, great question. I fell into the C trap.

the m<0 is a lot more significant that I thought.
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