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In the xy-plane above, the line segment PQ is bisected at right angles

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PKN
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In the xy-plane above, the line segment PQ is bisected at right angles [#permalink] New post   11 Aug 2018, 05:11
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In the xy-plane above, the line segment PQ is bisected at right angles by the line y = -x. The line segment QR (not shown) is bisected at right angles by the y - axis. What are the co-ordinates of point R?

A. (5,4)
B. (-4,-5)
C. (4,-5)
D. (-5,-4)
E. (4,5)

Source:- Time4education
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E

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In the xy-plane above, the line segment PQ is bisected at right angles [#permalink] New post   13 Dec 2018, 12:56
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PKN wrote:
In the xy-plane above, the line segment PQ is bisected at right angles by the line y = -x. The line segment QR (not shown) is bisected at right angles by the y - axis. What are the co-ordinates of point R?

A. (5,4)
B. (-4,-5)
C. (4,-5)
D. (-5,-4)
E. (4,5)

Source:- Time4education


This is based on the mirroring concept

1.A(a,b) when perpendicularly bisected by y=-x the mirror image of that point is B(-b,-a)

2.Mirror image of A(a,b) through y axis is B(-a,b)

3.Mirror image of A(a,b) through x axis is B(a,-b)

4.A(a,b) when perpendicularly bisected by y=x the mirror image of that point is B(b,a)

Points A and B are such that their midpoint lies on the line bisecting the AB line segment.

You can observe this in an xy plane by trying it out on a point.

Hence,

P(-5,4) --> mirror image through y=-x --> Q(-4,5)--> mirror image through y axis --> R(4,5)

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Please leave a kudos if this is helpful. Thanks!

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Re: In the xy-plane above, the line segment PQ is bisected at right angles [#permalink] New post   11 Aug 2018, 08:12
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PKN wrote:
In the xy-plane above, the line segment PQ is bisected at right angles by the line y = -x. The line segment QR (not shown) is bisected at right angles by the y - axis. What are the co-ordinates of point R?

A. (5,4)
B. (-4,-5)
C. (4,-5)
D. (-5,-4)
E. (4,5)

Source:- Time4education



Since PQ is bisected, Q is (-4,5) as P is (-5,4)
Now QR is bisected by X axis, so the line is x=4 and y =5
(4,5)
E
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Re: In the xy-plane above, the line segment PQ is bisected at right angles [#permalink] New post   13 Sep 2018, 07:31
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chetan2u could you explain this a little more?
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Re: In the xy-plane above, the line segment PQ is bisected at right angles [#permalink] New post   13 Dec 2018, 11:45
Can you please explain this in detail?
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Re: In the xy-plane above, the line segment PQ is bisected at right angles [#permalink] New post   05 May 2020, 20:55
PKN wrote:
In the xy-plane above, the line segment PQ is bisected at right angles by the line y = -x. The line segment QR (not shown) is bisected at right angles by the y - axis. What are the co-ordinates of point R?

A. (5,4)
B. (-4,-5)
C. (4,-5)
D. (-5,-4)
E. (4,5)

Source:- Time4education


Given:
1. In the xy-plane above, the line segment PQ is bisected at right angles by the line y = -x.
2. The line segment QR (not shown) is bisected at right angles by the y - axis.
Asked: What are the co-ordinates of point R?

Attachment:
Screenshot 2020-05-06 at 9.24.20 AM.png
Screenshot 2020-05-06 at 9.24.20 AM.png [ 41.38 KiB | Viewed 2062 times ]


1. In the xy-plane above, the line segment PQ is bisected at right angles by the line y = -x.
Since Q is the mirror image of P(-5,4) w.r.t.
y=-x; Q=(-4,5)

2. The line segment QR (not shown) is bisected at right angles by the y - axis.
Since R is the mirror image of Q w.r.t x=0
R= (4,5)

IMO E
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Re: In the xy-plane above, the line segment PQ is bisected at right angles [#permalink]
05 May 2020, 20:55
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