IS THIS A RIGHT

Question

AB¯¯¯¯¯¯¯¯ is rotated 100° clockwise about A. Then AB¯¯¯¯¯¯¯¯ is rotated 30° counterclockwise about B. What is the image of A as a composition of transformations?

A. (r(100,A)∘r(−30,B))(A)

B. (r(−100,A)∘r(30,B))(A)

C.(r(−30,A)∘r(100,B))(A)

D.(r(30,B)∘r(−100,A))(A)

Answer 1

Based on the way the question is stated, Point A and Point B exist to form a straight line.

Point A, I will take it as the origin. Imagine a unit circle. it will start as (0,0) Point A and (1,0) Point B.

A line along the x-axis.

Now, rotate clockwise 100 degrees, now Point B will be located in the 3rd Quadrant. Point A is still at (0,0). Again, rotate the line 30 counter clockwise but about Point A.

Reminder, Point A saw Point B move downward. Then Point B saw Point A move upward. Therefore, Clockwise is Negative and Counter-Clockwise is Positive. In the order of movement, B moved first then A moved.

Answer will be in the form:

r(30,B) ∘ r(-100,A)(A)