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In the rectangular coordinate system, the line y = x is the [#permalink]
 15 May 2012, 21:23
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In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C? A. (-3;-2) B. (-2; 3) C. (3;-2) D. (2;-3) E. (2; 3)
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Re: Cordinates of a point [#permalink]
15 May 2012, 22:30
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Given : 1> y = x is the perpendicular bisector of segment AB 2> x = 0 (y-axis) is the perpendicular bisector of segment BC 3> If the coordinates of point A are (3, 2) Combining 1 and 3, we can deduce that point B is the reflection of point A in the Axis Bisector (y = x) => Coordinates of Point B would be reverse of A and that is (2, 3) Note : here reflection is in X=Y , so x -coordinate and y - coordinate would exchange their places. So we can say : 4> If the coordinates of point B are (2, 3) Combining 3 and 4, we can deduce that point C is the reflection of point B in the Y Axis (x = 0) line => Coordinates of Point C would be reverse of B and that is (-2, 3) Note : here reflection is in Y axis , so sign of x -coordinate would change while sign of y coordinate would remain same. Hope it makes sense.
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Re: In the rectangular coordinate system, the line y = x is the [#permalink]
16 May 2012, 00:12
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In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C? A. (-3;-2) B. (-2; 3) C. (3;-2) D. (2;-3) E. (2; 3) Since the line y=x is the perpendicular bisector of segment AB, then point B is the mirror reflection of point A around the line y=x, so its coordinates are (2, 3). The same way, since the y-axis is the perpendicular bisector of segment BC then the point C is the mirror reflection of point B around the y-axis, so its coordinates are (-2, 3). Answer: B. The question becomes much easier if you just draw a rough sketch: Attachment: 
Point C.png [ 13.36 KiB | Viewed 1931 times ]
Now, you can simply see that options A, C, and D (blue dots) just can not be the right answers. As for option E: point (2, 3) coincides with point B, so it's also not the correct answer. Only answer choice B remains. Answer: B.
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Re: In the rectangular coordinate system, the line y = x is the [#permalink]
20 Jun 2012, 12:24
Hi Bunuel,
How did you deduce that the line AB perpendicular to y=x is a mirror reflection..Can you throw some more light on it???
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Re: In the rectangular coordinate system, the line y = x is the [#permalink]
20 Jun 2012, 23:17
abdulzeus wrote: Hi Bunuel,
How did you deduce that the line AB perpendicular to y=x is a mirror reflection..Can you throw some more light on it??? Hi, Since, line (y=x) is perpendiculare bisector of AB, points A & B should be equidistant from y=x. Thus, would be the mirror reflection. Regards,
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Re: In the rectangular coordinate system, the line y = x is the [#permalink]
02 Aug 2012, 12:24
@Bunuel : Isn't thr an algebric way to solve this problem ?
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Re: In the rectangular coordinate system, the line y = x is the [#permalink]
02 Aug 2012, 12:39
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(I am trying to solve this using substitution, not thinking of it in terms of reflection across lines)
In a rectangular coordinate system, the line y=x is the perpendicular bisector of segment AB and the x-axis is the perpendicular bisector of segment BC. If the coordinates of point A are (2,3), what are the coordinates of point C?
A) (-3,-2)
B) (-3, 2)
C) (2, -3)
D) (3, -2)
E) (2,3)
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Re: Coordinate system [#permalink]
29 Aug 2012, 00:45
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Re: In the rectangular coordinate system, the line y = x is the [#permalink]
31 Aug 2012, 10:59
enigma123 wrote: In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C?
A. (-3;-2)
B. (-2; 3)
C. (3;-2)
D. (2;-3)
E. (2; 3) Hey enigma123, An alternate way of solving this would be by visualization. First, we plot the line y=x and the point A(3,2) in our graph. a) Since we are given that AB is the perpendicular bisector of the line y=x, we can deduce from the figure that the value of the 'x' co-ordinate of point B must be positive and less than the value of the 'x' co-ordinate of point A. From this we can eliminate choices A,B and C b) Also, we can deduce by observation that the 'y' co-ordinate of point B is positive (since B lies above the X axis) From this we can eliminate choice D From a) and b), we now know that point B lies in the first quadrant. Only option that remains is E Cheers! Spare a second and gift me some KUDOS! 
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Re: In the rectangular coordinate system, the line y = x is the
[#permalink]
31 Aug 2012, 10:59
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