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?Reflection over the x-axis

Question

Reflection over the y-axis
Rotation 180 degrees about the origin
Translation 6 units down

Answer 1

To determine which transformation was applied to the rectangle, we need to analyze the changes in the vertices' coordinates.

The original rectangle has vertices:

• (2, 3)
• (5, 3)
• (5, 6)
• (2, 6)

After the transformation, the new rectangle has vertices:

• (2, -3)
• (5, -3)
• (5, -6)
• (2, -6)

Let's compare the original and new coordinates:

1. The x-coordinates remain the same for both rectangles: 2 and 5.
2. The y-coordinates change from positive to negative:
   • The original y-coordinates are 3 and 6.
   • The new y-coordinates are -3 and -6.

This indicates that the points were reflected across the x-axis, which changes the sign of the y-coordinates while keeping the x-coordinates the same.

Thus, the transformation applied is reflection over the x-axis.