Which transformation will be equivalent to rotating a figure 180° counterclockwise? a) reflecting over the line y = x. b) reflecting over the line y = -x. c) reflecting over the x-axis and the y-axis. d) translating left 3 units and down 5 units.

If we have given coordinates of the image are in form (h,k).

The resulting coordinates of image rotation of 180° around the origin would be (-h,-k).

We have rule (h,k) ---> (-h,-k).

We can see that x-coordinate is being multiplied by -1 and then y-coordinate is also being multiplied by -1.

Above rule could be break into two parts.

We can see in first step, (h,k) ---> (-h,k) is being reflecting over the x-axis and

in second step (-h,k) >  (-h,-k) is being reflecting over the y-axis.

256

Step-by-step explanation:

(5x4)x2 = 40

(5x12)x2 = 60

(4x12)x2 = 96

40+60+96 = 256