Question

A rectangle with vertices at (2,3), (5,3), (5,6), and (2,6) is transformed to a rectangle with vertices at (2,−3), (5,−3), (5,−6), and (2,−6). Which transformation was applied?
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1 point
Reflection over the x-axis
Reflection over the y-axis
Rotation 180 degrees about the origin
Translation 6 units down

Answer 1

To determine the transformation applied to the rectangle, let's analyze the original and transformed vertices:

Original vertices:
- (2, 3)
- (5, 3)
- (5, 6)
- (2, 6)

Transformed vertices:
- (2, -3)
- (5, -3)
- (5, -6)
- (2, -6)

Notice how each y-coordinate of the original vertices has changed from positive to negative:
- The y-coordinates of the original vertices are 3 and 6.
- The y-coordinates of the transformed vertices are -3 and -6.

This indicates that the transformation reflected the original rectangle across the x-axis, changing the sign of each y-coordinate.

Thus, the correct transformation is:
**Reflection over the x-axis.**