Question

A square with vertices at (3,3), (6,3), (6,6), and (3,6) is transformed to a square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6). Which transformation was applied?
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1 point
Translation 6 units left and 6 units down
Translation 6 units right and 6 units up
Rotation 180 degrees about the origin
Rotation 90 degrees clockwise about the origin

Answer 1

To determine the transformation applied to the square with vertices at (3,3), (6,3), (6,6), and (3,6) to reach the square with vertices at (−3,−3), (−6,−3), (−6,−6), and (−3,−6), we can analyze the change in the coordinates of the vertices.

The original vertices are:
- (3, 3)
- (6, 3)
- (6, 6)
- (3, 6)

The transformed vertices are:
- (−3, −3)
- (−6, −3)
- (−6, −6)
- (−3, −6)

To compare, we can see what happens to each vertex of the original square when we apply a potential transformation.

### **Checking for Rotation 180 degrees about the origin:**
A point (x, y) when rotated 180 degrees about the origin becomes (-x, -y).
1. (3, 3) becomes (-3, -3)
2. (6, 3) becomes (-6, -3)
3. (6, 6) becomes (-6, -6)
4. (3, 6) becomes (-3, -6)

All vertices are correctly transformed to the new positions.

### **Other transformations:**
- **Translation 6 units left and 6 units down:**
- (3, 3) -> (-3, -3)
- (6, 3) -> (0, -3) (not matching)

- **Translation 6 units right and 6 units up:**
- (3, 3) -> (9, 9) (not matching)

- **Rotation 90 degrees clockwise about the origin:**
- (3, 3) -> (3, -3) (not matching)

Therefore, the correct transformation applied to change the square's position is:

**Rotation 180 degrees about the origin.**