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In the rectangular coordinate system above, the line y = x [#permalink]
27 Dec 2012, 04:05

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A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

73% (02:33) correct
27% (01:42) wrong based on 441 sessions

Attachment:

Reflcetion.png [ 8.39 KiB | Viewed 4715 times ]

In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (2,3), what are the coordinates of point C ?

In the rectangular coordinate system above, the line y = x [#permalink]
27 Dec 2012, 04:13

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In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (2,3), what are the coordinates of point C ?

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 (3, 2). In any mirror reflection around the line y = x, the x-coordinate and the y-coordinate of a point become interchanged.

The same way, since the x-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 3, -2). In any mirror reflection around the x-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes.

Answer: D.

The question becomes much easier if you just draw a rough sketch:

Attachment:

Reflection2.png [ 10.75 KiB | Viewed 4526 times ]

Now, you can simply see that only D can be the correct answer.

Re: In the rectangular coordinate system above, the line y = x [#permalink]
30 Oct 2013, 05:25

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From question stem, we can know that, Point C will be in the 4th quadrant (X,-Y), which comes down to option C&D. B is perpendicular to A (2,3). Hence co-ordinates of B will be (3,2). C & B are parallel to Y-axis and are on the same line. Hence co-ordinates of C will share same X-co-ordinate. (3,-Y). i.e. Ans. choice D

*I have difficult time understanding Co-ordiante geometry, hence try to solve in the simple way. This was my approach and was able to get ans. in less than a Minute.

Re: In the rectangular coordinate system above, the line y = x [#permalink]
09 Dec 2014, 09:46

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Re: In the rectangular coordinate system above, the line y = x [#permalink]
16 Feb 2015, 10:03

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Quote:

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 (-3, 2)

Hi Bunuel,

Isn't x-axis a perpendicular bisector of line BC and the coordinates of C are (3,-2). Looks like some typos in the explanation?

Re: In the rectangular coordinate system above, the line y = x [#permalink]
16 Feb 2015, 10:12

Expert's post

aj0809 wrote:

Quote:

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 (-3, 2)

Hi Bunuel,

Isn't x-axis a perpendicular bisector of line BC and the coordinates of C are (3,-2). Looks like some typos in the explanation?

Thanks, AJ

Yes. Edited the typo. Thank you. _________________

Now, coming back to this question, you are given data to find the positions of B and C.

"the line y = x is the perpendicular bisector of segment AB (not shown)"

You know that point A is (2, 3). We need the mirror image of A on y = x. Imagine drawing a line perpendicular to y = x from A. It will intersect y = x at (2.5, 2.5), a point 0.5 below and 0.5 to the right. So the point B will be 0.5 further to the right and 0.5 down giving us the coordinate (2.5 + .5, 2.5 - .5) i.e. (3, 2).

For C, you are given that " the x-axis is the perpendicular bisector of segment BC (not shown)"

A line perpendicular to x axis will be x = 0 i.e. vertical line. So C's x coordinate will be the same as B's x coordinate. Since B is 2 above the x axis, C will be 2 below the x axis. So C will be at (3, -2) _________________

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