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

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VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1009
WE: Supply Chain Management (Energy and Utilities)
In the xy-plane above, the line segment PQ is bisected at right angles  [#permalink]

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11 Aug 2018, 05:11
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00:00

Difficulty:

65% (hard)

Question Stats:

57% (02:16) correct 43% (02:49) wrong based on 92 sessions

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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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Math Expert
Joined: 02 Aug 2009
Posts: 7752
Re: In the xy-plane above, the line segment PQ is bisected at right angles  [#permalink]

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11 Aug 2018, 08:12
3
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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Manager
Joined: 28 Jun 2018
Posts: 74
Re: In the xy-plane above, the line segment PQ is bisected at right angles  [#permalink]

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13 Sep 2018, 07:31
1
chetan2u could you explain this a little more?
Manager
Joined: 27 Oct 2017
Posts: 64
Re: In the xy-plane above, the line segment PQ is bisected at right angles  [#permalink]

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13 Dec 2018, 11:45
Can you please explain this in detail?
Intern
Joined: 20 Nov 2018
Posts: 21
Location: India
In the xy-plane above, the line segment PQ is bisected at right angles  [#permalink]

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13 Dec 2018, 12:56
2
1
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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In the xy-plane above, the line segment PQ is bisected at right angles   [#permalink] 13 Dec 2018, 12:56
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