Figure abcd is parallelogram with point a (-3,2) what rule would rotate the figure 90 counterclockwise

(x, y) ⇒ (-y, x)

A point at y=1 on the y-axis will rotate to the point x = -1 on the x-axis when it is rotated 90° CCW about the origin. Hence the value of x for the image point is the opposite of the y-value of the original point.

A point at x=1 on the x-axis will rotate to the point y=1 on the y-axis when it is rotated 90° CCW about the origin. Hence the value of y for the image point is the x-value of the original point.

In summary, ...

... (x, y) ⇒ (-y, x)

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Comment on rotation matrices

The rotation matrix for rotatation through the angle θ CCW about the origin is ...

When θ = 90°, this matrix becomes ...

and multiplication by coordinates (x, y) gives ...

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet