Question
Which of the following mapping is used for a 270 degree (counterclockwise) rotation?
a. (x, y) ---> (y, -x)
b. (x, y) ---> (-y, x)
c. (x, y) ---> (-y, -x)
d. (x, y) ---> (-x, -y)
a. (x, y) ---> (y, -x)
b. (x, y) ---> (-y, x)
c. (x, y) ---> (-y, -x)
d. (x, y) ---> (-x, -y)
Answers
GPT-4o mini
To determine which mapping corresponds to a 270-degree counterclockwise rotation, we can analyze the effect of such a rotation on a point \((x, y)\).
A 270-degree counterclockwise rotation can also be viewed as a 90-degree clockwise rotation. The effect of a 90-degree clockwise rotation on the point \((x, y)\) is given by:
\[
(x, y) \rightarrow (y, -x)
\]
Now, we can match this with the options provided:
a. \((x, y) \rightarrow (y, -x)\) - This is the 90-degree clockwise rotation.
b. \((x, y) \rightarrow (-y, x)\) - This represents a 90-degree counterclockwise rotation.
c. \((x, y) \rightarrow (-y, -x)\) - This represents a 180-degree rotation.
d. \((x, y) \rightarrow (-x, -y)\) - This represents a 180-degree rotation.
Since a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation, the correct mapping for a 270-degree counterclockwise rotation is:
**a. (x, y) ---> (y, -x)**
A 270-degree counterclockwise rotation can also be viewed as a 90-degree clockwise rotation. The effect of a 90-degree clockwise rotation on the point \((x, y)\) is given by:
\[
(x, y) \rightarrow (y, -x)
\]
Now, we can match this with the options provided:
a. \((x, y) \rightarrow (y, -x)\) - This is the 90-degree clockwise rotation.
b. \((x, y) \rightarrow (-y, x)\) - This represents a 90-degree counterclockwise rotation.
c. \((x, y) \rightarrow (-y, -x)\) - This represents a 180-degree rotation.
d. \((x, y) \rightarrow (-x, -y)\) - This represents a 180-degree rotation.
Since a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation, the correct mapping for a 270-degree counterclockwise rotation is:
**a. (x, y) ---> (y, -x)**