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Three of the four vertices of a rectangle in the xy-coordinate plane a

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GMAT 1: 800 Q51 V51
Three of the four vertices of a rectangle in the xy-coordinate plane a  [#permalink]

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New post 10 May 2018, 17:54
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Three of the four vertices of a rectangle in the xy-coordinate plane are ( -3, 10), ( 2, 10), and (2, 1). What is the fourth vertex?

A) (-3,1)
B) (-3,2)
C) (-2,10)
D) (2,-3)
E) (3,10)
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Three of the four vertices of a rectangle in the xy-coordinate plane a  [#permalink]

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New post 10 May 2018, 20:59
(-3,10) (2,10)
.............
. .
. .
............. (2,1)

Missing coordinate will take x value of(-3,10) and y value of (2,1) coordinates

So those will remain same

A is answer

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GMAT 1: 800 Q51 V51
Re: Three of the four vertices of a rectangle in the xy-coordinate plane a  [#permalink]

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New post 11 May 2018, 06:28
push12345 wrote:
(-3,10) (2,10)
.............
. .
. .
............. (2,1)

Missing coordinate will take x value of(-3,10) and y value of (2,1) coordinates

So those will remain same

A is answer

Posted from my mobile device



Can you ellaborate little more on this?
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Three of the four vertices of a rectangle in the xy-coordinate plane a  [#permalink]

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New post 11 May 2018, 08:37
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alanforde800Maximus wrote:
Three of the four vertices of a rectangle in the xy-coordinate plane are ( -3, 10), ( 2, 10), and (2, 1). What is the fourth vertex?

A) (-3,1)
B) (-3,2)
C) (-2,10)
D) (2,-3)
E) (3,10)

Attachment:
coordrectangle.png
coordrectangle.png [ 8.4 KiB | Viewed 882 times ]

alanforde800Maximus

From the sketch (does not take long)
The figure is a rectangle
(parallel/perpendicular sides, opposite side lengths are equal)
the fourth coordinate is at (-3, 1)

The fourth vertex, D

--must have an x-coordinate that
is exactly the same as Vertex A

-- must have a y-coordinate that
is exactly the same as Vertex C

Stated differently
The x- and y-coordinates without a "match"
are those of the fourth vertex


One missing side, AD, is vertical
It is parallel to the y-axis
The line it lies on is x = -3
We have three x coordinates: -3, 2, and 2

The x-coordinate without a "match"
is (-3, 10)
There is a vertical line at x = -3
The fourth vertex must lie on x = -3

We have three y coordinates: 1, 10, and 10
The y-coordinate that does not have a "match"
is (2, 1)
There is a horizontal side on line: y = 1
The fourth vertex must lie on y = 1

The fourth vertex is at (-3, 1)

Answer A

Hope that helps :-)
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Re: Three of the four vertices of a rectangle in the xy-coordinate plane a  [#permalink]

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Re: Three of the four vertices of a rectangle in the xy-coordinate plane a   [#permalink] 07 Aug 2019, 22:53
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