Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown:

(image)

Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?

A) Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 1 unit
B) Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 1 unit
C) Reflection about the x-axis followed by a translation to the left by 1 unit
D) Reflection about the y-axis followed by a translation to the right by 1 unit

What if you were asking this question? How would you explain it to yourself?

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.