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Magoosh GMAT Instructor G
Joined: 28 Dec 2011
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In a coordinate system, P = (2, 7) and Q = (2, –3). Which c  [#permalink]

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4
21 00:00

Difficulty:   95% (hard)

Question Stats: 39% (02:39) correct 61% (02:43) wrong based on 240 sessions

### HideShow timer Statistics In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be the coordinates of R if PQR is an isosceles triangle?

I. (12, –3)
II. (–6, –9)
III. (–117, 2)

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

For a set of seven other challenging Coordinate Geometry problems, as well as the OE with diagrams for this question, see:
http://magoosh.com/gmat/2014/challengin ... questions/

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Mike McGarry
Magoosh Test Prep

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GMAT 1: 760 Q49 V42 GMAT 2: 760 Q49 V42 Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c  [#permalink]

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2
PQ's length is 10.

1. QR is also 10.
2. Pythagorean triplet, again QR is 10.
3. y=2 is a bisector of QR so anything on this line will create an isosceles triangle.

So E I, II and III
GMATH Teacher P
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Joined: 12 Oct 2010
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Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c  [#permalink]

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1
stoneshwar wrote:
PQ's length is 10.

1. QR is also 10.
2. Pythagorean triplet, again QR is 10.
3. y=2 is a bisector of QR so anything on this line will create an isosceles triangle.

So E I, II and III

Perfect! Those arguments deserve the corresponding image (attached).

Regards,
Fabio.
Attachments 25Set18_4w.gif [ 11.79 KiB | Viewed 1087 times ]

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c  [#permalink]

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fskilnik wrote:
stoneshwar wrote:
PQ's length is 10.

1. QR is also 10.
2. Pythagorean triplet, again QR is 10.
3. y=2 is a bisector of QR so anything on this line will create an isosceles triangle.

So E I, II and III

Perfect! Those arguments deserve the corresponding image (attached).

Regards,
Fabio.

2 Questions here:
1. Can we apply the triplet rule without knowing for sure if 1 angle in 90? Or other way round can this triplet be applied on any triangle?
2. How can we rule out the possibility that PR = QR?

TIA
GMATH Teacher P
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Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c  [#permalink]

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PinakiRDas wrote:
2 Questions here:
1. Can we apply the triplet rule without knowing for sure if 1 angle in 90? Or other way round can this triplet be applied on any triangle?
2. How can we rule out the possibility that PR = QR?

Hi, PinakiRDas.

1. No! In the figure in the middle, the fact that there is a 90-degrees angle "formed" by the sides with lengths 6 and 8 is necessary to be able to conclude that the other side (the hypotenuse) is 10 units of length. More explicitly: you have a (non-right) triangle with sides 6,8 and 10.1, for instance.
2. Any equilateral triangle is also an isosceles triangle. An isosceles triangle, by definition, has (at least) two sides with same lengths.

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c   [#permalink] 26 Sep 2018, 19:51
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# In a coordinate system, P = (2, 7) and Q = (2, –3). Which c   