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Which of the following points is reflect to y=x at (2,1)? [#permalink]
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06 Jan 2017, 01:45
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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)
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Re: Which of the following points is reflect to y=x at (2,1)? [#permalink]
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06 Jan 2017, 08:20
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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 SMG610F using GMAT Club Forum mobile app



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Re: Which of the following points is reflect to y=x at (2,1)? [#permalink]
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08 Jan 2017, 17:12
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==> You can figure out a point reflecting to y=x by substituting –y to xcoordinate and –x to ycoordinate. 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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09 Jan 2017, 09:37
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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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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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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 coordinate 2 becomes y coordinate and y cordinate 1 becomes x coordinate. 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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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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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/inthexycoo ... 43502.htmlhttp://gmatclub.com/forum/intherectan ... 32646.htmlhttp://gmatclub.com/forum/thecoordinat ... 27769.htmlhttp://gmatclub.com/forum/thelinerepr ... 27770.htmlhttp://gmatclub.com/forum/ifpointaco ... 41972.htmlhttp://gmatclub.com/forum/intherectan ... 88473.htmlhttp://gmatclub.com/forum/intherectan ... 44774.htmlhttp://gmatclub.com/forum/thelinerepr ... 87573.htmlhttps://gmatclub.com/forum/intherecta ... 29932.htmlHope 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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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 = (y1)/(x+2) y1 = 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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06 Sep 2017, 12:52
A.
Consider a circle with the centre in origin and radiusend 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]
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10 Jan 2018, 02:13
Sherlock221b wrote: 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 SMG610F using GMAT Club Forum mobile appyour 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.



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Re: Which of the following points is reflect to y=x at (2,1)? [#permalink]
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10 Jan 2018, 02:29
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 ScottTargetTestPrephello, does your method apply to the general form of any linear equatation y = mx + n ?



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Re: Which of the following points is reflect to y=x at (2,1)? [#permalink]
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12 Jan 2018, 11:38
chesstitans 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 ScottTargetTestPrephello, does your method apply to the general form of any linear equatation y = mx + n ? 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 45degree angle with the negative xaxis). 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 arisesfor example, reflect (1, 2) over y = 3x + 4we deal with it individually using concepts of coordinate geometry rather than a formula that few people can memorize.
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