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In the rectangular coordinate system, the line y = x is the

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In the rectangular coordinate system, the line y = x is the [#permalink] New post 15 May 2012, 20:23
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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)
[Reveal] Spoiler: OA

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Re: Cordinates of a point [#permalink] New post 15 May 2012, 21:30
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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] New post 15 May 2012, 23:12
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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
Point C.png [ 13.36 KiB | Viewed 2858 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] New post 20 Jun 2012, 11:24
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] New post 20 Jun 2012, 22:17
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.

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Re: In the rectangular coordinate system, the line y = x is the [#permalink] New post 02 Aug 2012, 11:24
@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] New post 02 Aug 2012, 11:39
Expert's post
smartmanav wrote:
@Bunuel : Isn't thr an algebric way to solve this problem ?


Sure there is but the solution above is less time consuming.

Coordinate Geometry chapter of Math Book (coordinate-geometry-87652.html) could help you to figure out algebraic solution if still needed.
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Coordinate system [#permalink] New post 28 Aug 2012, 18:57
(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] New post 28 Aug 2012, 23:45
Expert's post
egiles wrote:
(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)


Merging topics. Please ask if anything remains unclear.

Similar question to practice: in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html

Hope it helps.
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Re: In the rectangular coordinate system, the line y = x is the [#permalink] New post 31 Aug 2012, 09:59
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

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Re: In the rectangular coordinate system, the line y = x is the   [#permalink] 31 Aug 2012, 09:59
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