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

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Intern
Joined: 27 Apr 2016
Posts: 11
A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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Updated on: 02 Sep 2018, 01:04
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Difficulty:

15% (low)

Question Stats:

84% (00:46) correct 16% (00:43) wrong based on 31 sessions

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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, 00:06.
Last edited by Bunuel on 02 Sep 2018, 01:04, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Joined: 15 Aug 2016
Posts: 149
Location: India
Concentration: Technology, Operations
GMAT 1: 690 Q49 V35
WE: Operations (Consulting)
Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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02 Sep 2018, 00:18
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.
Director
Joined: 18 Jul 2018
Posts: 502
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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02 Sep 2018, 00:21
1
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.

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Joined: 31 Jul 2017
Posts: 505
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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Updated on: 02 Sep 2018, 07:54
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, 00:25.
Last edited by rahul16singh28 on 02 Sep 2018, 07:54, edited 1 time in total.
Intern
Joined: 27 Apr 2016
Posts: 11
Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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02 Sep 2018, 07:51
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.

Thanks you so much for this.
Math Expert
Joined: 02 Aug 2009
Posts: 7108
Re: A square is formed by connecting points (4, 0), (0, 4), (4, 8), and (8  [#permalink]

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02 Sep 2018, 20:55
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 &nbs [#permalink] 02 Sep 2018, 20:55
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