Question

rotation of 180 clockwise
translation 4 units down
reflection over x - axis
dilation with scale factor of 2

Explanation:

To determine the transformation, we analyze each option:

• Rotation of 180° clockwise: A 180° rotation would change the coordinates in a way that doesn't match the vertical shift seen here.
• Translation 4 units down: Looking at a point like \( A(-3,1) \) and \( A'(-3,-3) \), the change in the \( y \)-coordinate is \( 1 - (-3)=4 \) (downward). Similarly, other points (e.g., \( B(-3,3) \) to \( B'(-3,-1) \), \( C(-2,3) \) to \( C'(-2,-1) \), \( D(-2,1) \) to \( D'(-2,-3) \)) also show a vertical shift of 4 units down.
• Reflection over x - axis: A reflection over the \( x \)-axis would change \( (x,y) \) to \( (x, -y) \). For \( A(-3,1) \), this would be \( (-3,-1) \), not \( (-3,-3) \), so this is incorrect.
• Dilation with scale factor of 2: Dilation would change the size, but the shape and position (relative to horizontal) don't show scaling; the size remains the same.

Answer:

translation 4 units down