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Which of the following points reflect to y=-x at (-3,2)?

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by Vincen » Wed Oct 11, 2017 5:44 pm
Which of the following points reflect to y=-x at (-3,2)?

A. (-2, 3)
B. (2,-3)
C. (3,2)
D. (3,-2)
E. (2,3)

The OA is A.

Do I need to make a graph or is there another way to solve this PS question?
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by EconomistGMATTutor » Thu Oct 12, 2017 2:02 pm
Vincen wrote:Which of the following points reflect to y=-x at (-3,2)?

A. (-2, 3)
B. (2,-3)
C. (3,2)
D. (3,-2)
E. (2,3)

The OA is A.

Do I need to make a graph or is there another way to solve this PS question?
Hi Vincen,
Lets take a look at your question.
We don't need to make a graph to find the reflected point.

Just remember the rules.
The reflection of the point (x,y) across the line y = x is the point (y, x).
The reflection of the point (x,y) across the line y = -x is the point (-y, -x).

In this question we need to reflect the point (-3,2) over y = -x,
so it will be (-y, -x) i.e.
(-2, -(-3)) = (-2, 3)

Therefore, Option A is correct.
Hope this helps.

I am available if you'd like any follow up.
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by Matt@VeritasPrep » Thu Oct 12, 2017 8:45 pm
Since our equation is y = -x, just take the original coordinates and plug them into the formula.

original x = -3
original y = 2

new y = -(original x) = -(-3) = 3
new x = -1 * (original y) = (-1) * 2 = -2

That gives us a reflected (x, y) of (-2, 3), and we're set.
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by Matt@VeritasPrep » Thu Oct 12, 2017 8:47 pm
Another way to think about this: y = -x means "take y, multiply by -1, and move it to x".

If our first y is 2, we thus:

take y: y = 2
multiply by -1: y = -2
move it to x: x = -2

And if our first x is -3, we do the same, since y = -x is the same as -y = x:

take x: x = -3
multiply by -1: x = 3
move it to y: y = 3

That leaves us with x = -2 and y = 3, so we're done.
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by Matt@VeritasPrep » Thu Oct 12, 2017 8:48 pm
Final thought: this isn't a properly formatted GMAT problem. "reflect to" isn't really grammatical, and the prompt is too ambiguous to appear on the exam. I'm also not sure that the test has ever explicitly asked about a reflection across an axis or a line -- I can't recall such a question -- but I could be wrong, and if I am, I'm sure some other expert will chime in to one up me! :)
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