Question

(–4, 9), (–4, –3), (–1, –3), and
(–1, 9). What is the area?

Answer 1

Answer: 36

That's a 12 by 3 rectangle. We can tell from the differences of the points, called the direction vectors.

A(-4,9), B(–4, –3), C(–1, –3), D(–1, 9)

AB=B-A=(-4 - -4, -3 - 9) = (0, -12)

BC=(-1 - -4, -3 - -3) = (3, 0)

CD = (-1 - -1, 9 - -3) = (0, 12)

DA = (-4 - -1, 9 - 9) = (-3, 0)

We see the equal and opposite direction vectors from opposite sides, so this is definitely a parallelogram. The zeros indicate the directions are parallel to the x and y axes, so it's a rectangle. In particular it's 3×12 so area 36.

Answer 2

Assuming the 4th coordinate is supposed to be (-1, -9) then the area is 18

Explanation:

Plot it on a graph and it makes a very weird quadrilateral. But if the 4th coordinate (-1, 9)'s y coordinate is actual -9 then it makes a rectangle. I'm going to assume that's a typo and it is a rectangle so it would be a 3 by 6 rectangle. 3*6 is 18.