Question

The coordinates for a point and its image are Q (-3,-5) and Q' (5, -3). Based on the mapping rules for rotations, which transformation occurred? (1 point) Responses a 180-degree rotation a 180-degree rotation a 270-degree (counterclockwise) rotation a 270-degree (counterclockwise) rotation a 90-degree (counterclockwise) rotation a 90-degree (counterclockwise) rotation a reflection across the x-axis a reflection across the x-axis

Answer 1

To determine the transformation that occurred from point Q (-3, -5) to its image Q' (5, -3), let's analyze the changes in the coordinates:

1. Original Point Q: (-3, -5)
2. Transformed Point Q': (5, -3)

We can look for patterns based on common transformations:

• Reflection across the x-axis: Would change (-3, -5) to (-3, 5), which does not match.

• Reflection across the y-axis: Would change (-3, -5) to (3, -5), which does not match.

• 180-degree rotation: A 180-degree rotation around the origin takes (x, y) to (-x, -y). So:

  • (Q) (-3, -5) would transform to (3, 5), which does not match.

• 90-degree counterclockwise rotation: Taking (x, y) to (-y, x):

  • (-3, -5) would transform to (5, -3), which matches Q'.

• 270-degree counterclockwise rotation: Taking (x, y) to (y, -x):

  • (-3, -5) would transform to (-5, 3), which does not match.

based on the analysis, the transformation that took place from point Q (-3, -5) to point Q' (5, -3) is a 90-degree counterclockwise rotation.