hich of the following mappings is used for a 270-degree (counterclockwise) rotation?(1 point)

Question

Responses

(x,y)→(−x,−y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma negative y right parenthesis

(x,y)→(−y,x)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma x right parenthesis

(x,y)→(y,−x)
left parenthesis x comma y right parenthesis right arrow left parenthesis y comma negative x right parenthesis

(x,y)→(−y,−x)

Answer 1

To determine the mapping for a 270-degree counterclockwise rotation, we can analyze the effect of this rotation on the coordinates (x, y):

1. A 90-degree counterclockwise rotation transforms (x, y) to (-y, x).
2. A 180-degree counterclockwise rotation transforms (x, y) to (-x, -y).
3. A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation, which transforms (x, y) to (y, -x).

From your options, the correct mapping corresponding to a 270-degree counterclockwise rotation is:

\((x,y) \rightarrow (y, -x)\)

So, the answer is:

\((x,y) \rightarrow (y, -x)\) (the third option).