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

This topic has expert replies
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members
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?

User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

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.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

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.

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

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.

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

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! :)