Triangle RST and its image, triangle R’S’T’, are graphed on the coordinate grid below. Which rotation, using the origin as the center of rotation, transformed RST to R’S’T’?
A. a 90° clockwise rotation
B. a 90° counterclockwise rotation
C. a 45° clockwise rotation
D. a 45° counterclockwise rotation

B. a 90º counterclockwise rotation

Step-by-step explanation:

You can tell that it moves 90º and it moves in a counterclockwise direction because from RST to R’S’T’ it moves left to right. That is counterclockwise when you look it up.

Hope this helps!!! :

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.

the 4th choice is the correct one

step-by-step explanation: