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In a coordinate system, P = (2, 7) and Q = (2, –3). Which c

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

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New post 01 Aug 2014, 13:25
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A
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C
D
E

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Question Stats:

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

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New post 01 Aug 2014, 22:57
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
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Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c  [#permalink]

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New post 25 Sep 2018, 12:39
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
25Set18_4w.gif [ 11.79 KiB | Viewed 1087 times ]


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

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New post 26 Sep 2018, 18:37
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
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Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c  [#permalink]

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New post 26 Sep 2018, 19:51
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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Re: In a coordinate system, P = (2, 7) and Q = (2, –3). Which c   [#permalink] 26 Sep 2018, 19:51
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