"Reflected around" is incorrect language. Something is either
reflected across or
rotated around.
When something is reflected across the x-axis, that means that it appears in the "opposite" spot above/below the x-axis relative to where it used to be. So, a point that was previously at (5, 8) would appear below the x-axis at (5, -8). A point that was previously at (-4, -9) would appear above the x-axis at (-4, 9). In each case, the x-coordinate remains the same, while the y-coordinate switches its sign. There is a vertical change, but no horizontal change.
On the other hand, when something is reflected across the y-axis, that means that it appears in the "opposite" spot left/right the y-axis relative to where it used to be. So, a point that was previously at (5, 8) would appear to the left of the y-axis at (-5, 8). A point that was previously at (-4, -9) would appear to the right of the y-axis at (4, -9). In each case, the y-coordinate remains the same, while the x-coordinate switches its sign. There is a horizontal change, but no vertical change.
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)
Statement 1 tells us that the line itself goes through (3, 4), which is the reflection over the x-axis of (3, -4). If a line goes through (3, 4), it cannot also go through (5, 4) unless it is a horizontal line with slope 0, which this is not.
Statement 2 tells us that the line itself goes through (5, 3), which is the reflection over the y-axis of (-5, 3). If a line goes through (5, 3), it cannot also go through (5, 4) unless it is a vertical line with no slope, which this is not.
In each case, we can answer with a definitive NO, so each statement is sufficient. D.
