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# In the coordinate plane, rectangle WXYZ has vertices at (–2

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Joined: 18 Apr 2015
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Kudos [?]: 1027 [0], given: 4631

In the coordinate plane, rectangle WXYZ has vertices at (–2 [#permalink]  24 May 2017, 01:47
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Question Stats:

77% (01:11) correct 22% (01:21) wrong based on 22 sessions

In the coordinate plane, rectangle WXYZ has vertices at (–2, –1), (–2, y), (4, y), and (4, –1). If the area of WXYZ is 18, what is the length of its diagonal?

A) $$3 \sqrt{2}$$

B) $$3 \sqrt{3}$$

C) $$3 \sqrt{5}$$

D) $$3 \sqrt{6}$$

E) $$3 \sqrt{7}$$
[Reveal] Spoiler: OA

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Director
Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 330 [0], given: 66

Re: In the coordinate plane, rectangle WXYZ has vertices at (–2 [#permalink]  10 Oct 2017, 09:15
Since we have two points as (-1, -2) and (-1, 4) who are in line, we easily compute the length of one of the sides of the rectangle as 4-(-2) = 6.

Then, given the area, we can compute the other side of the rectangle as 18/6 = 3.

Know, the diagonal of the rectangle is the hypotenuse of the right triangle of legs 3 and 6, thus it can be computed as 6^2+3^9 = 45 = 3sqrt(5).

Intern
Joined: 27 Oct 2018
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Kudos [?]: 12 [0], given: 27

Re: In the coordinate plane, rectangle WXYZ has vertices at (–2 [#permalink]  02 Nov 2018, 12:42
Answer should be root(40) i.e. 2 * root(10)
Re: In the coordinate plane, rectangle WXYZ has vertices at (–2   [#permalink] 02 Nov 2018, 12:42
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