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# In the xy-plane, the sides of a certain rectangle are

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Director
Affiliations: FRM Charter holder
Joined: 02 Dec 2006
Posts: 729
Schools: Stanford, Chicago Booth, Babson College
In the xy-plane, the sides of a certain rectangle are [#permalink]

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14 Feb 2007, 06:00
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50% (01:01) correct 50% (00:39) wrong based on 4 sessions

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In the xy-plane, the sides of a certain rectangle are parallel to the axes. If one of the vertices of the rectangle is (-1,-2), what is the perimeter of the rectangle?
(1) One of the vertices of the rectangle is (2, -2).
(2) One of the vertices of the rectangle is (2, 3).
SVP
Joined: 01 May 2006
Posts: 1796

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14 Feb 2007, 07:05
(B) for me

1 vertex is at (-1,-2) and the sides are parallel to the axes implies that 2 sides are supported by the lines x=-1 and y=-2.

To calculate the perimeter, we need to konw either:
> the diagonally opposed vertex to (-1,-2) (Basically, the point to know has to be on a x different from -1 and on a y different from -2)
or
> 2 vertices : one on x=-1 and one on y=-2

Otherwise, we remain with a fluctuating size for 2 sides of the rectangle.

From 1
(2,-2) is on the same line y=-2. We miss 1 point to conclude. (Fig 1)

INSUFF

From 2
(2,3) is neither on x=-1 nor on y=-2. Bingo. (Fig 2)

SUFF.
Attachments

Fig1_Stat1_1 vertex at 2,-2.gif [ 2.52 KiB | Viewed 1120 times ]

Fig2_Stat2_1 vertex at 2,3.gif [ 2.55 KiB | Viewed 1142 times ]

Last edited by Fig on 15 Feb 2007, 00:08, edited 2 times in total.
Manager
Joined: 29 Nov 2006
Posts: 83

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14 Feb 2007, 07:35
if we used either (-1,3) and (2,-2), they would have the same perimeter.

I would go wit B.
Manager
Joined: 12 Feb 2006
Posts: 115

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14 Feb 2007, 21:31
Man, I love Fig's graph paper.

It makes everything so clear.
SVP
Joined: 01 May 2006
Posts: 1796

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15 Feb 2007, 00:10
bz9 wrote:
Man, I love Fig's graph paper.

It makes everything so clear.

Yes... a draw of XY plan can be very useful
15 Feb 2007, 00:10
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