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# The points (1,6) and (7,-2) are two vertices of one diagonal of a squa

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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The points (1,6) and (7,-2) are two vertices of one diagonal of a squa  [#permalink]

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09 Oct 2018, 18:33
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:03) correct 35% (01:53) wrong based on 37 sessions

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[Math Revolution GMAT math practice question]

The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square?

A. 16
B. 25
C. 32
D. 36
E. 50

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 18 Jul 2018 Posts: 379 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa [#permalink] ### Show Tags 09 Oct 2018, 18:38 Distance between the vertices of the diagonal is given by sqrt(36+64) = 10. If the side of a sqaure is a, then diagonal will be a*sqrt(2). Diagonal = 10. Side becomes 10/sqrt(2). Area = 100/2 = 50. E is the answer Posted from my mobile device _________________ When you want something, the whole universe conspires in helping you achieve it. Director Joined: 06 Jan 2015 Posts: 519 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa [#permalink] ### Show Tags 09 Oct 2018, 18:55 MathRevolution wrote: [Math Revolution GMAT math practice question] The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square? A. 16 B. 25 C. 32 D. 36 E. 50 The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane So Diagonal = $$\sqrt{(36+64)}$$==> 10 Area = $$1/2(d^2)$$ Area =1/2(10^2) =50 Hence E _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Manager Joined: 26 Apr 2011 Posts: 56 Location: India GPA: 3.5 WE: Information Technology (Computer Software) Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa [#permalink] ### Show Tags 11 Oct 2018, 00:30 NandishSS wrote: MathRevolution wrote: [Math Revolution GMAT math practice question] The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square? A. 16 B. 25 C. 32 D. 36 E. 50 The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane So Diagonal = $$\sqrt{(36+64)}$$==> 10 Area = $$1/2(d^2)$$ Area =1/2(10^2) =50 Hence E I have a silly question. Can we not use the given co-ordinates to find the length of sides? But that will produce 2 different lengths and that will not be a square! I am missing some funda here. Please help _________________ Do What Your Heart Says.... Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6535 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa [#permalink] ### Show Tags 11 Oct 2018, 00:37 => The length of the diagonal of the square is $$\sqrt{{ (7-1)^2 + (6-(-2))^2 }} = √100 = 10.$$ The side-length of the square is $$\frac{10}{√2} = 5 √2$$ since the side-length of a square is equal to the length of its diagonal divided by $$√2$$. Thus, the area of the square is $$(5 √2)^2 = 50.$$ Therefore, E is the answer. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa  [#permalink]

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11 Oct 2018, 01:16
Hey MrCleantek

Given: The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. Not vertices of sides

Quote:
I have a silly question. Can we not use the given co-ordinates to find the length of sides? But that will produce 2 different lengths and that will not be a square! I am missing some funda here. Please help

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Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa  [#permalink]

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11 Oct 2018, 01:33
NandishSS wrote:
Hey MrCleantek

Given: The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. Not vertices of sides

Quote:
I have a silly question. Can we not use the given co-ordinates to find the length of sides? But that will produce 2 different lengths and that will not be a square! I am missing some funda here. Please help

But the sides can be derived from the vertices right since its a square? I mean draw perpendicular lines from there and you would have the sides.
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Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa  [#permalink]

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18 Oct 2018, 17:24
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square?

A. 16
B. 25
C. 32
D. 36
E. 50

By the distance formula, the length of the diagonal of the square is:

d = √[(7 - 1)^2 + (-2 - 6)^2] = √[36 + 64] = √100 = 10.

Recall that the area of a square, given a diagonal of length d, is A = d^2/2. Thus, the area of the square is:

A = 10^2/2 = 100/2 = 50

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Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa &nbs [#permalink] 18 Oct 2018, 17:24
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