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Bunuel
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A square in the coordinate plane has vertices whose y-coordinates are 23 Apr 2019, 13:17
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95% (hard)

Question Stats:

28% (02:44) correct 72% (02:09) wrong based on 212 sessions

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A square in the coordinate plane has vertices whose y-coordinates are 0, 1, 4, and 5. What is the area of the square?

(A) 16
(B) 17
(C) 25
(D) 26
(E) 27
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B
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A square in the coordinate plane has vertices whose y-coordinates are 07 Oct 2019, 00:57
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Let's play with Geometry
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A square in the coordinate plane has vertices whose y-coordinates are 27 Apr 2019, 01:29
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Bunuel
A square in the coordinate plane has vertices whose y-coordinates are 0, 1, 4, and 5. What is the area of the square?

(A) 16
(B) 17
(C) 25
(D) 26
(E) 27
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coordiante ; (x1,0) , (x2,1), (x3,4 ), (x4,5)
difference in y coordinate point ; 4-0 ; 4 and 5-1 ; 4
use distance formula to find length of each side ; √4^2+1^2 ; √17
area ; 17
IMO B
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A square in the coordinate plane has vertices whose y-coordinates are 01 May 2019, 02:06
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Answer is C as 5 is the length of one side of the square.
A=s^2
5^2=25

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A square in the coordinate plane has vertices whose y-coordinates are 06 Oct 2019, 07:44
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coordiante ; (x1,0) , (x2,1), (x3,4 ), (x4,5)
difference in y coordinate point ; 4-0 ; 4 and 5-1 ; 4
use distance formula to find length of each side ; √4^2+1^2 ; √17
area ; 17

Hi Mr Bunuel,


Not able to comprehend this particular concept. Can you pl eloborate.
Thanking you in anticipation
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A square in the coordinate plane has vertices whose y-coordinates are Updated on: 24 Oct 2019, 21:35
Originally posted by TestPrepUnlimited on 06 Oct 2019, 12:06.
Last edited by TestPrepUnlimited on 24 Oct 2019, 21:35, edited 2 times in total.
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Bunuel
A square in the coordinate plane has vertices whose y-coordinates are 0, 1, 4, and 5. What is the area of the square?

(A) 16
(B) 17
(C) 25
(D) 26
(E) 27
Show more

All y-coordinates are different therefore it must be a tilted square. The major clue, in this case, is that there are two pairs of points with y-coordinates that have the difference of one: 0, 1 and 4, 5 have the same difference and they make a pair of parallel lines. You can also pair the points with y-coordinates of 0, 4 and 1, 5 and make up the other pair of parallel lines. Therefore the length is sqrt(4^2 + 1^2) = sqrt(17) and the area is 17.
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A square in the coordinate plane has vertices whose y-coordinates are 08 Oct 2019, 00:58
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testprepunlimited and satya2029...

thank you very much for this gr8 explanation.
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A square in the coordinate plane has vertices whose y-coordinates are 25 Apr 2021, 09:05
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satya2029
Let's play with Geometry
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Another method could be the bigger square PQRS - 4 right triangles i.e. 5*5 - 4*(0.5 * 1 * 4) = 17
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A square in the coordinate plane has vertices whose y-coordinates are 26 Apr 2021, 02:35
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Can someone please explain the solution ?
I am not able to understand how do we get the sqr(1) in sqroot(sqr(4) + sqr(1)) in the above mentioned solutions.
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A square in the coordinate plane has vertices whose y-coordinates are 13 Mar 2025, 22:43
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