In the coordinate plane, square ABCD has vertices at A (3, 7), B (3, 1

Question

In the coordinate plane, square ABCD has vertices at A(3, 7), B(3, 12), C(8, x), D(8, y). What is the area of ABCD ?

A) 16

B) 20

C) 25

D) 30

E) 36

pushpitkc · Answer

Formula used: 
Distance between 2 points A(x1,y1) and B(x2,y2) is  \sqrt{(x2 - x1)^2 + (y2 - y1)^2} 
 
In the square ABCD, the distance between points A(3,7) and B(3,12) is either the side
or the diagonal of the square. Now, AB =  \sqrt{(3 - 3)^2 + (12 - 7)^2} = \sqrt{5^2} = 5

If AB is the diagonal of the square, the area will be  (\frac{5}{\sqrt{2}})^2  =  \frac{25}{2} (Not an answer option)
Therefore, the area of the square ABCD =  AB^2 = 5^2 = 25  (Option C)

gmatzpractice · Answer

C 
Height is 12-7 
Width is 8-3 
Area is 25

SajjitaKundu · Answer

I am sorry, but how can AB be the diagonal? A and B are adjacent sides right?Although it is not given, isn't it explicitly implied? Since AB for me is a side, whose length is 5. Clear cut, the area becomes 5*5 = 25.

Bunuel  am I right?

sumitkrocks · Answer

From the given information we can infer that two vertex of the square are on line X=3 and other two on X=8 ...from this we can infer side must be 8-3=5

Hence area is 5^2=25 Answer is "C"

PAVITHRAN · Answer

If are you double minded like me. Just plot it out

Ans 25

PKN · Answer

Area of square= a^2 , where a is the length of side.

Point A(3,7) and B(3,12) have the same 'x' coordinate value.Hence, they are separated by a distance of 5 unit(=12-7=5).

Therefore, AB=5 unit=side of the square.

Now, area of square= 5^2 =25 sq unit

Ans. (C)

GyMrAT · Answer

Given a square ABCD with vertices A(3, 7), B(3, 12), C(8, x), D(8, y)

Hence, Points A & B lie on line x = 3, with distance between them as (12-7) = 5 units

Points C & D lie on line x = 8, hence we can say that segment AB is a side of the square.

Hence Area of square =  5^2  = 25

Answer C.

Thanks,
GyM

alphastallion · Answer

I have used the distance between two point for AB to get 5,is it right approach.
thanks

GyMrAT · Answer

alphastallion  yes it is.

gmatzpractice · Answer

The distance formula is unnecessary and time-consuming here.

GyMrAT · Answer

Yes, I agree. A simple subtraction of y co ordinates is sufficient.

Thanks,
GyM

In the coordinate plane, square ABCD has vertices at A (3, 7), B (3, 1

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In the coordinate plane, square ABCD has vertices at A (3, 7), B (3, 1

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards