Question

Find the area of the parallelogram with vertices a(−3, 1), b(−1, 4), c(3, 2), and d(1, −1).

Answer 1

To find the area of a parallelogram, we need to find the magnitude of the cross product of the vectors representing two sides of the parallelogram.

Let's choose vectors AB and AD as the sides of the parallelogram.

AB = (−1, 4) − (−3, 1) = (2, 3)

AD = (1, −1) − (−3, 1) = (4, −2)

Now let's find the magnitude of the cross product of these vectors:

|AB x AD| = |(2)(−2) − (3)(4)| = |-4 - 12| = -14

So the area of the parallelogram is -14 square units.