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

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

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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)
[Reveal] Spoiler: OA

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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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New post 06 Jan 2017, 08:20
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

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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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==> 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
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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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MathRevolution wrote:
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)


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
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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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New post 20 Feb 2017, 18:23
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"

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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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New post 02 Sep 2017, 07:34
MathRevolution wrote:
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)


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

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

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New post 02 Sep 2017, 22:34
ScottTargetTestPrep wrote:
MathRevolution wrote:
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)


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


Hi Sir ,

Can you give theory regarding these kinds of problems .

Regards,
Arvind
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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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New post 03 Sep 2017, 03:34
arvind910619 wrote:
ScottTargetTestPrep wrote:
MathRevolution wrote:
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)


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


Hi Sir ,

Can you give theory regarding these kinds of problems .

Regards,
Arvind


No specific theory on this but you can check similar questions to practice:
http://gmatclub.com/forum/in-the-xy-coo ... 43502.html
http://gmatclub.com/forum/in-the-rectan ... 32646.html
http://gmatclub.com/forum/the-coordinat ... 27769.html
http://gmatclub.com/forum/the-line-repr ... 27770.html
http://gmatclub.com/forum/if-point-a-co ... 41972.html
http://gmatclub.com/forum/in-the-rectan ... 88473.html
http://gmatclub.com/forum/in-the-rectan ... 44774.html
http://gmatclub.com/forum/the-line-repr ... 87573.html
https://gmatclub.com/forum/in-the-recta ... 29932.html

Hope it helps.
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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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New post 05 Sep 2017, 16:31
arvind910619 wrote:
ScottTargetTestPrep wrote:
MathRevolution wrote:
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)


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


Hi Sir ,

Can you give theory regarding these kinds of problems .

Regards,
Arvind


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

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Re: Which of the following points is reflect to y=-x at (-2,1)? [#permalink]

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New post 06 Sep 2017, 12:52
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:)

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Re: Which of the following points is reflect to y=-x at (-2,1)?   [#permalink] 06 Sep 2017, 12:52
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