Question

Which of the following mappings is used for a 270-degree (counterclockwise) rotation?
A. (x,y) → (-y,x)
B. (x,y) → (y, -x)
C. (x,y) → (-x,-y)
D. (x,y) → (-y, -x)

Answer 1

To determine which mapping corresponds to a 270-degree (counterclockwise) rotation, we can analyze how the coordinates (x, y) transform.

A 270-degree counterclockwise rotation can also be described as a 90-degree clockwise rotation. The effect of a 90-degree clockwise rotation on the coordinates (x, y) is to transform them to (y, -x).

Now, let's look at the options provided:

A. (x,y) → (-y,x)
B. (x,y) → (y,-x)
C. (x,y) → (-x,-y)
D. (x,y) → (-y,-x)

From the analysis, we see that:

- Option B, \( (x, y) → (y, -x) \), is the correct mapping for a 270-degree counterclockwise rotation.

Thus, the answer is **B. (x,y) → (y, -x)**.