Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin. U(-7,-4)
V(-7,-1)
W(-10,-2)

How to
U'( , ), V'( , ), W'( , )

The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

U'(-4, 7), V'(-1, 7), W'(-2, 10)

Step-by-step explanation:

When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.

Thus,

The rule to rotate a point P(x, y)  after a rotation 270° counterclockwise around the origin is:

P(x, y) → P'(y, -x)

In our case, we have the points

U(-7,-4)

V(-7,-1)

W(-10,-2)

Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

P(x, y)          →        P'(y, -x)

U(-7,-4)        →        U'(-4, 7)

V(-7, -1)        →        V'(-1, 7)

W(-10, -2)    →         W'(-2, 10)

Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

U'(-4, 7), V'(-1, 7), W'(-2, 10)

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

ian gonna lie that is way to much