Which of the following points is reflect to y=-x at (-2,1)?

Question

A. (-1, 2) B. (1,-2) C. (2,1) D. (2,-1) E. (1,2)

ScottTargetTestPrep · Accepted Answer

When reflecting a point across the line y = -x, we can follow this rule:

If coordinates (a,b) are reflected across the line y = -x, then the new reflected coordinates are (-b, -a).

Thus, when (-2,1) is reflected across the line y = -x, the new reflected coordinates are (-1,2).

Answer: A

Sherlock221b · Answer

Y=-x is a line in second quadrant. 
And point (-2,1) lies below it so its reflection to y=-× will be opposite but in the same quadrant .
So D

Sent from my SM-G610F using  GMAT Club Forum mobile app

MathRevolution · Answer

==> You can figure out a point reflecting to y=-x by substituting –y to x-coordinate and –x to y-coordinate. Then, (-2,1) --> (-1, -(-2))=(-1,2) is derived.

Hence, the answer is A.
Answer: A

Nunuboy1994 · Answer

Which of the following points is reflect to y=-x at (-2,1)?

A. (-1, 2) B. (1,-2) C. (2,1) D. (2,-1) E. (1,2)

Okay so I think "C" is the trap answer in this question. (2,1) reflects (-2,1) but we're dealing with y= "-x"

Arsh4MBA · Answer

When reflected about line y=-x the x co-ordinate -2 becomes y co-ordinate and y cordinate 1 becomes x co-ordinate.
Since (-2,1) is in 2nd quadrant we interchange signs annd get (-1,2)

So  ans: A

arvind910619 · Answer

Hi Sir ,

Can you give theory regarding these kinds of problems .

Regards,
Arvind

Bunuel · Answer

KLC · Answer

Quick Theory: Let the reflected point be (x,y). The line joining points (-2,1) and (x,y) will be perpendicular to the mirror line.

Mirror line => y = -x has slope = -1. Therefore the line joining reflected and actual points will have slope = 1.

Using the slope rise/run form for the line joining original and reflected point we get:

1 = (y - 1)/(x - (-2))

1 = (y-1)/(x+2)

y-1 = x + 2

y = x + 3

Only Option A satisfies this condition

AlexGmat2017 · Answer

A.

Consider a circle with the centre in origin and radius-end point in (-2,1).
Graph y = -x is a diameter to this circle, so our answer comes from symmetry with respect to this diameter (y = -x).
+you may play with triangular equalities/symmetries and so on:)

chesstitans · Answer

your method is brilliant, but since gmat does not allow test takers to bring rulers, ones will find difficult to estimate the quadrant of a point given annoying locations.
Also, your method is correct, but your calculation is incorrect. OA is A.

chesstitans · Answer

ScottTargetTestPrep 
hello, does your method apply to the general form of any linear equatation y = mx + n ?

ScottTargetTestPrep · Answer

Hi chesstitans,

No, it doesn't apply to any line in the form of y = mx + b (for any value of m and b). The formula works here for y = -x because y = -x is a special line (it makes a 45-degree angle with the negative x-axis). The same goes for lines y = x, y = 0, and x = 0 because they are special lines. However, it doesn't apply to any line in general. That said, there is a formula for reflecting a point of a line in the form of y = mx + b. However, that formula is not easy to memorize, so when a problem arises--for example, reflect (1, 2) over y = 3x + 4--we deal with it individually using concepts of coordinate geometry rather than a formula that few people can memorize.

Kritisood · Answer

https://magoosh.com/math/coordinate-geo ... ate-plane/

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Which of the following points is reflect to y=-x at (-2,1)?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following points is reflect to y=-x at (-2,1)?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards