Find the area of the parallelogram whose three of the vertices are (1, -2), (2, 3) and (-3, 2) in order. also find its fourth vertex .

Area = 24 square unit,

Fourth vertex = (-4, -3)

Step-by-step explanation:

Suppose we have a parallelogram ABCD,

Having vertex A(1, -2), B(2, 3), and C(-3, 2),

Let D(x,y) be the fourth vertex of the parallelogram,

∵ The diagonals of a parallelogram bisect each other,

Thus, the midpoint of AC = midpoint of  BD

By comparing,

Thus, the fourth vertex is (-4, -3),

Now, the area of the parallelogram ABCD = 2 × area of triangle ABC (Because both diagonals divide the parallelogram in two equal triangles)

Area of a triangle having vertex , and is,

So, the area of triangle ABC

Hence, the area of the parallelogram ABCD = 2 × 12 = 24 square unit.

you forgot an image

step-by-step explanation:

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.