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In a rectangular coordinate syste, what is the are of a...

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by AAPL » Tue Dec 12, 2017 2:21 pm
In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-4, 1), (1, 1), (1, -3) and (-4, -3)?

A. 16
B. 20
C. 24
D. 25
E. 30

The OA is B.

Experts, I need a suggestion about how can I solve this PS question. I have an idea but I think that it's the long way, it is the following,

I can take one vertex of the rectangle like reference and determinate the distance between it and 2 of the vertices that converge with it, then this two distances can be the long and width of the renctangle, right? and once with it I can determinate the rectangle's area.

Thanks!
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by Jay@ManhattanReview » Tue Dec 12, 2017 9:08 pm
AAPL wrote:In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-4, 1), (1, 1), (1, -3) and (-4, -3)?

A. 16
B. 20
C. 24
D. 25
E. 30

The OA is B.

Experts, I need a suggestion about how can I solve this PS question. I have an idea but I think that it's the long way, it is the following,

I can take one vertex of the rectangle like reference and determinate the distance between it and 2 of the vertices that converge with it, then this two distances can be the long and width of the renctangle, right? and once with it I can determinate the rectangle's area.

Thanks!
Hi,

What you described would work. The rectangle would have a length of |-4| + 1 = 5 and the width of |-3| + 1 = 4. Thus, the area of the rectangle = 5*4 = 20 sq unit.

The correct answer: B

Hope this helps!

-Jay
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by EconomistGMATTutor » Wed Dec 13, 2017 8:22 am
In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-4, 1), (1, 1), (1, -3) and (-4, -3)?

A. 16
B. 20
C. 24
D. 25
E. 30

The OA is B.
Hi AAPL,
Let's take a look at your question.

The co-ordinates of the rectangle are given as
(-4, 1), (1, 1), (1, -3) and (-4, -3)
If we take the first two coordinates (-4, 1), (1, 1),
We can see that their y coordinate the the same it means that these two points will form a horizontal line, which will give us the length of the rectangle.
$$Length\ =\ \left|-4-1\right|=\left|-5\right|=5$$

Similarly, now choose any two points that have same x coordinate to find the width of the rectangle.
We can take (1, 1), (1, -3)
These two points represent a vertical line.
$$Width\ =\ \left|1-\left(-3\right)\right|=\left|1+3\right|=\left|4\right|=4$$
Now we can find the area of the rectangle.
$$Area=Length\times Width$$
$$Area=5\times4=20$$

Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.
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