Parallelogram abcd has vertex coordinates a(0, 1), b(1, 3), c(4, 3), and d(3, 1). it is translated 2 units to the right and 3 units down and then rotated 180 clockwise around the origin. what are the coordinates of a?

 The correct option is (C). (-2, 2).

Step-by-step explanation:  Given that the co-ordinates of the vertices of parallelogram ABCD are A(0, 1), B(1, 3), C(4, 3), and D(3, 1). The parallelogram ABCD is translated 2 units to the right and 3 units down and then rotated 180 clockwise around the origin.

We are to find the co-ordinates of the vertex A after the transformation.

We know that if the point (x, y) is translated a units right and b units down, then its new co-ordinates will be (x + a, y - b).

So, the co-ordinates of point A after translation of 2 units to the right and 3 units down are

(0 + 2,  1 - 3) = (2, -2).

Now, a rotation of 180° clockwise will change the co-ordinates (x, y) to (-x, -y).

Therefore, the final co-ordinates of point A are

(2, -2)  ⇒ (-2, 2).

Thus, the new co-ordinates of A are (-2, 2).

Option (C) is CORRECT.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.