Polygon abcd goes through a sequence of rigid transformations to form polygon a′b′c′d′. the sequence of transformations involved is a reflection across the , followed by a reflection across the line

Step-by-step explanation:

The polygon ABCD showed in the image attached is first reflected across the y = x line, from the second quadrant to the fourth quadrant. This reflection will result like the second image.

Then, it's reflect across the y-axis, which in terms of lines would be x = 0 line. This reflection will be like the last position showed in the first image, it's a common reflection with y-axis as a mirror.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.