Find the angle of the rotations for the graphs below. The center of rotation is the origin, and the darker image is the preimage. Your answer will be 90°, 270 degrees, or 180 degrees.

  a. 90°

  b. 180°

  c. 180°

Step-by-step explanation:

For these problems there is a bit of a shortcut you can take. Each figure is entirely within one quadrant, and the rotation is said to be by 90° (one quadrant), 180° (two quadrants), or 270° (three quadrants) clockwise.

a. The image is in the adjacent clockwise quadrant, so rotation is 90°.

b, c. The image is in the diagonally opposite quadrant, so rotation is 180°.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2