Given parallelogram \(PARK\): Prove graphically and algebraically that a clockwise rotation of \(270°\) about the origin has an equivalent counterclockwise rotation. In your final answer, name the equivalent counterclockwise rotation and show all of your work. On your graph, label the following:

parallelogram \(PARK\) and the coordinates of all four of its vertices
parallelogram \(P'A'R'K'\) and the coordinates of all four of its vertices
center of rotation and its coordinate
the invisible circle of rotation, its radius and the length of the radius
use arrows to show the clockwise movement of the parallelogram

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula

she will travel a distance in the range of 3 - 11 miles

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

15.36 per mile

but forgot to round

i am pretty sure