Problem Solving

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 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.