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

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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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New post 09 Oct 2018, 18:33
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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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Re: The points (1,6) and (7,-2) are two vertices of one diagonal of a squa  [#permalink]

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New post 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

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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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New post 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
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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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New post 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 :(
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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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New post 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
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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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New post 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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New post 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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New post 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

Answer: E
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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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