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We are given coordinates of the triangle: A(2,2), B(7,1) and C(8,-4).

We need to rotated 90° counterclockwise about the origin.

In order to find the new coordinates of rotatation 90°counterclockwise about the origin, we can apply rule (h, k) ---> (-k,h).

Where (h,k) are the coordinates of original image on axes and (-k,h) are the coordinates of rotated image.

In resulting coordinates of the image first swap the x and y coordinates of the original image and then make the sign opposite of each x-coordinate.

On applying rule (h, k) ---> (-k,h), we get

A(2,2) --> A'(-2,2)

B(7,1) --> B'(-1,7)

C(8,-4) --> C'(4,8)

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a