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