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Nanobotstv
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GMAT 1: 800 Q51 V51
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Three of the four vertices of a rectangle in the xy-coordinate plane a 10 May 2018, 17:54
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

94% (01:00) correct 6% (01:29) wrong based on 453 sessions

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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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A
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push12345
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Three of the four vertices of a rectangle in the xy-coordinate plane a 10 May 2018, 20:59
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(-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
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Nanobotstv
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Three of the four vertices of a rectangle in the xy-coordinate plane a 11 May 2018, 06:28
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push12345
(-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
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Can you ellaborate little more on this?
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generis
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Three of the four vertices of a rectangle in the xy-coordinate plane a 11 May 2018, 08:37
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alanforde800Maximus
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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Attachment:
coordrectangle.png
coordrectangle.png [ 8.4 KiB | Viewed 8224 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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Three of the four vertices of a rectangle in the xy-coordinate plane a 03 Jun 2023, 01:30
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To find the fourth vertex of the rectangle, we need to understand the properties of a rectangle. A rectangle has opposite sides that are equal in length and parallel to each other.

Given that three vertices of the rectangle are (-3, 10), (2, 10), and (2, 1), we can determine the missing fourth vertex by observing the pattern.

Since the opposite sides of a rectangle are parallel, the y-coordinate of the missing fourth vertex should be equal to the y-coordinate of the second vertex, which is 10.

Looking at the given options, only option E) (3, 10) satisfies this condition, where the y-coordinate is 10.
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