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A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8

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A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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New post Updated on: 02 Sep 2018, 02:04
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A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8, 4). What is the area of the square?

A) 6
B) 16
C) 24
D) 25
E) 32

Originally posted by archimaitreya25 on 02 Sep 2018, 01:06.
Last edited by Bunuel on 02 Sep 2018, 02:04, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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New post 02 Sep 2018, 01:18
If you want you can draw a rough graph of it.
Take any two coordinates that would be adjacent if we draw a square.
Lets take (4,0) and (8,4).
Lets use distance formula is this. i.e root((x2-x1)^2 +(y2-y1)^2)
=> root((8-4)^2 + (4-0)^2)
=> root(16+16)
=>root32
=> 4root2. All sides equal in square.
=> area=4root2 X 4root2=> 32.
Please revert for any doubts.!!
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Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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New post 02 Sep 2018, 01:21
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The distance between the two points is given by \(\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}\)

Lets consider points (4,0) and (0,4)

\(\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}\)
= \(\sqrt{(0-4)^2+(4-0)^2}\)
= \(\sqrt{32}\)
= 4\(\sqrt{2}\)

Side of the square = 4\(\sqrt{2}\)

Area = \({Side}^2\) = 32.

E is the answer.
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A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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New post Updated on: 02 Sep 2018, 08:54
1
archimaitreya25 wrote:
Hi,

Can anyone help solve the below mentioned problem for me and explain it as well.

A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8, 4). What is the area of the square?

A) 6
B) 16
C) 24
D) 25
e) 32

The way I computed, my answer was 16. However, that is incorrect.

TIA


Hi archimaitreya25

Consider the points (4,0) & (4,8).. If you draw the points on axes... 8 will be the diagonal between the points \((4,0) & (4,8).\)
Now, for any square Diagonal - \(\sqrt{2}a\) (a is side of Square). Now, we have -
\(\sqrt{2}a = 8 --> a = 4\sqrt{2}\)
Area \(= a^2 = 32..\)
Hope this is clear.
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Originally posted by rahul16singh28 on 02 Sep 2018, 01:25.
Last edited by rahul16singh28 on 02 Sep 2018, 08:54, edited 1 time in total.
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Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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New post 02 Sep 2018, 08:51
Afc0892 wrote:
The distance between the two points is given by \(\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}\)

Lets consider points (4,0) and (0,4)

\(\sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2}\)
= \(\sqrt{(0-4)^2+(4-0)^2}\)
= \(\sqrt{32}\)
= 4\(\sqrt{2}\)

Side of the square = 4\(\sqrt{2}\)

Area = \({Side}^2\) = 32.

E is the answer.


Thanks you so much for this.
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Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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New post 02 Sep 2018, 21:55
archimaitreya25 wrote:
A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8, 4). What is the area of the square?

A) 6
B) 16
C) 24
D) 25
E) 32


Mark the coordinates on x-y axis..
you can see that the side of square is \(\sqrt{4^2+4^2}=\sqrt{32}\)

Area of square = \(side^2=\sqrt{32}^2=32\)

E
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Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8   [#permalink] 02 Sep 2018, 21:55
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