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In the rectangular coordinate system, the line y = x is the [#permalink]
15 May 2012, 20:23

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Difficulty:

25% (low)

Question Stats:

73% (02:07) correct
26% (01:04) wrong based on 79 sessions

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)

Re: Cordinates of a point [#permalink]
15 May 2012, 21:30

1

This post received KUDOS

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.

Re: In the rectangular coordinate system, the line y = x is the [#permalink]
15 May 2012, 23:12

2

This post received KUDOS

Expert's post

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 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.

Re: In the rectangular coordinate system, the line y = x is the [#permalink]
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.
_________________

(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)

Re: Coordinate system [#permalink]
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.

Re: In the rectangular coordinate system, the line y = x is the [#permalink]
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

Cheers!

Spare a second and gift me some KUDOS!

gmatclubot

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