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

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

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...!!!
and i'm editing my previous post...!!!

Wow, great question. I fell into the C trap.

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