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 occured?

a. a reflection across the y-axis
b. a 180-degree rotation
c. a 90-degree (counterclockwise) rotation
d. a 270-degree (counterclockwise) rotation

1 answer

To determine the transformation that occurred from point Q(-3, -5) to point Q'(5, -3), we can analyze the coordinates:

  1. Original point: Q(-3, -5)
  2. Image point: Q'(5, -3)

Now, let's examine each option:

a. Reflection across the y-axis: Reflecting Q across the y-axis would change the x-coordinate to its opposite, giving us Q''(3, -5). This does not match Q'.

b. 180-degree rotation: To apply a 180-degree rotation around the origin, you negate both coordinates. For Q(-3, -5), we get Q''(3, 5), which does not match Q'.

c. 90-degree counterclockwise rotation: A 90-degree counterclockwise rotation transforms (x, y) into (-y, x). So, it would transform Q(-3, -5) into (5, -3), which matches Q'.

d. 270-degree counterclockwise rotation: A 270-degree counterclockwise rotation transforms (x, y) into (y, -x). Applying this to Q(-3, -5) gives us (-5, 3), which does not match Q'.

Based on the analysis, the correct transformation that occurred is:

c. a 90-degree (counterclockwise) rotation.