Question

Rotations as Functions Quick Check 1 of 51 of 5 Items Question Which of the following mappings is used for a 270-degree (counterclockwise) rotation?(1 point) Responses (x,y)→(−y,−x) left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma negative x 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)→(−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 y comma negative x right parenthesis Skip to navigation page 15 of 15 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the correct mapping for a 270-degree counterclockwise rotation, we can analyze how points move under this transformation.

A 270-degree counterclockwise rotation can also be viewed as a 90-degree clockwise rotation. Here's the effect of these rotations on the point (x, y):

1. 270-degree counterclockwise rotation (or 90-degree clockwise rotation):
   • The point (x, y) transforms to (y, -x).

Thus, the correct mapping for a 270-degree counterclockwise rotation is:

(x, y) → (y, -x)

Therefore, the answer is: (x,y)→(y,−x).