Data Sufficiency

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)

What does reflected mean?

"Reflected" like looking in a mirror. Since the slope is negative, we're looking at a line that is tilted to the left, like \.

When it's reflected across the x-axis (------), it would look like:

\
------
/

When it's reflected across the y-axis, it would look like:

|
|
\ | /
|
|

It's easier to draw than to explain

Yes vivian already explained, made it easy. answer shld be D

Hi how do you get D here. Please explain.

Hi Viv,

So the slope changes sign in a reflection? The exp. seems to imply that it doesn't.

VivianKerr wrote:"Reflected" like looking in a mirror. Since the slope is negative, we're looking at a line that is tilted to the left, like \.

When it's reflected across the x-axis (------), it would look like:

\


------
/

When it's reflected across the y-axis, it would look like:

|
|
\ | /
|
|

It's easier to draw than to explain

"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.

Thanks a lot Greg. Your reply was very helpful.

Each statement is sufficient to me

IMO.D

Good question .
Ans D

Thanks for the explanation, Greg.