The question should read as follows:
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 across the x-axis, line q passes through (3,-4)
(2) When it is reflected across the y-axis, line q passes through (-5,3)
When a line is REFLECTED ACROSS another line, we get a mirror image.
Statement 1: When it is reflected across the x-axis, line q passes through (3,-4)
If line Q contains point (a,b) and is reflected across the X-AXIS to yield line J, then line J contains point (a,-b).
In other words, when a point on a line is reflected across the x-axis, the x-coordinate STAYS THE SAME, while the y-coordinate CHANGES SIGN.
Here, since line J contains (3,-4), line Q must contain (3,4):
Since line Q contains (3,4), it cannot also contain (5,4).
SUFFICIENT.
Statement 2: When it is reflected across the y-axis, line q passes through (-5,3)
If line Q contains point (a,b) and is reflected across the Y-AXIS to yield line K, then line K contains point (-a,b).
In other words, when a point on a line is reflected across the y-axis, the y-coordinate STAYS THE SAME, while the x-coordinate CHANGES SIGN.
Here, since line K contains (-5,3), line Q must contain (5,3):
Since line Q contains (5,3), it cannot also contain (5,4).
SUFFICIENT.
The correct answer is
D.
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