Question

Find the area of the parallelogram with vertices a(−3, 0), b(−1, 3), c(5, 2), and d(3, −1).

Answer 1

To find the area of a parallelogram, we can use the formula: Area = base x height. By finding the lengths of the sides and the perpendicular distance, we can calculate the area of the parallelogram. In this case, the area is 8 units squared.

Step-by-step explanation:

To find the area of a parallelogram, we can use the formula:

Area = base x height

First, we need to find the base and height of the parallelogram. We can do this by finding the length of the two sides that form the base, and the perpendicular distance between the base and the opposite side.

Using the coordinates of the vertices: a(-3, 0), b(-1, 3), c(5, 2), and d(3, -1), we can find the lengths of the sides and the perpendicular distance.

Using the distance formula, we find: Side AB = sqrt((-1 - -3)^2 + (3 - 0)^2) = sqrt(8)

Side CD = sqrt((3 - 5)^2 + (-1 - 2)^2) = sqrt(9)

Perpendicular distance = sqrt((-1 - -3)^2 + (3 - 0)^2) = sqrt(8)

Now we can calculate the area using the formula:

Area = base x height = AB x Distance = sqrt(8) x sqrt(8) = 8 units squared.

Answer 2

|AD|=(3i-1j)-(-3i-0j)=3i-1j+3i+0j=6i-1j
|BA|=(-3i-0j)-(-1i+3j)=-3i-0j+1i-3j=-2i-3j

Area =|AD|x|BA|
= i j k
6 -1 0
-2 -3 0

= -1 0 i - 6 0 j + 6 -1 k
-3 0 -2 0 -2 -3

= 0 i - 0 j + (-18-2)k = -20 k

√(-20)² =20