Question

Which transformation will be equivalent to rotating a figure 270° counterclockwise? A) reflecting over the x-axis and the y-axis

B) translating left 3 units and down 5 units
C) Reflecting over the y-axis and then reflecting over the line y = x
D) Reflecting over the y-axis and then reflecting over the line y = -x

Answer 1

D) Reflecting over the y-axis and then reflecting over the line y = -x

Explanation:

When the figure is rotate clock-wise or anti clock-wise then the coordinate of figure is get changed and this new coordinate can be find on the basis of degree of rotation.

The rules of rotation is:

1. When rotation = 90° clock-wise, the vertices is get changed to (-y, x) from (x, y).
2. When rotation = 180° clock-wise, the vertices is get changed to (-x, -y) from (x, y).
3. When rotation = 270° clock-wise, the vertices is get changed to (y, -x) from (x, y).

Thus, Option (D) is correct option.

Answer 2

Reflection over the y-axis:
(x, y) ⇒ (-x, y)

Reflection of that over the line y = x:
(-x, y) ⇒ (y, -x)

Rotation counterclockwise by 270°:
(x, y) ⇒ (y, -x) . . . . . . equivalent to reflection over y, then over y=x.

The appropriate choice is ...
C) Reflecting over the y-axis and then reflecting over the line y = x.