The coordinates for a point and its image are Q(−3,−5)

Question

and Q′(5,−3)
. Based on the mapping rules for rotations, which transformation occurred?(1 point)
Responses

a 90-degree (counterclockwise) rotation
a 90-degree (counterclockwise) rotation

a −180
-degree (clockwise) rotation or a 180-degree (counterclockwise) rotation
a negative 180 -degree (clockwise) rotation or a 180-degree (counterclockwise) rotation

a 270-degree (counterclockwise) rotation
a 270-degree (counterclockwise) rotation

a −90
-degree (clockwise) rotation

Answer 1

To determine the transformation that occurred to go from point Q(−3,−5) to its image Q′(5,−3), we can analyze the transformations associated with the given rotation options.

1. 90-degree counterclockwise rotation: The formula for this transformation is (x, y) → (-y, x).

   • Applying this to Q(−3,−5):
     • Q(−3,−5) → (5, -3), which matches Q′(5, −3).
   • Thus, this transformation is a correct fit.

2. -180-degree (clockwise) rotation or a 180-degree (counterclockwise) rotation: The formula for 180-degree rotation is (x, y) → (-x, -y).

   • Applying this to Q(−3,−5):
     • Q(−3,−5) → (3, 5), which does not match Q′(5,−3).
   • Thus, this transformation does not fit.

3. 270-degree (counterclockwise) rotation (or 90-degree clockwise): The formula for this transformation is (x, y) → (y, -x).

   • Applying this to Q(−3,−5):
     • Q(−3,−5) → (-5, 3), which does not match Q′(5,−3).
   • Thus, this transformation does not fit.

4. -90-degree (clockwise) rotation (or 270-degree counterclockwise): The formula for this transformation is (x, y) → (y, -x).

   • As stated above, this transformation was analyzed, and it also does not match Q′(5,−3).

Based on the evaluations, the correct transformation that occurred from Q(−3,−5) to Q′(5,−3) is:

a 90-degree (counterclockwise) rotation.