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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
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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, 19:33
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Difficulty:

45% (medium)

Question Stats:

62% (01:25) correct 38% (01:45) wrong based on 81 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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 18 Jul 2018 Posts: 902 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, 19:38 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 _________________ Press +1 Kudo If my post helps! Director Joined: 06 Jan 2015 Posts: 641 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, 19:55 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: 60 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, 01:30 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: 7360 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, 01:37 => 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$149 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, 02:16
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, 02:33
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, 18:24
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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The points (1,6) and (7,-2) are two vertices of one diagonal of a squa  [#permalink]

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24 Nov 2018, 11:15
MrCleantek wrote:
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.

Yes, you can easily plot the sides with help of diagonal points or you can use the ratio formula for right angle isosceles triangle
($$x : x : x\sqrt{2}$$)
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The points (1,6) and (7,-2) are two vertices of one diagonal of a squa   [#permalink] 24 Nov 2018, 11:15
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