Question

rotation of 180 clockwise translation 4 units down reflection over x - axis dilation with scale factor of 2 reflection over y - axis rotation of 90 clockwise

Explanation:

To determine the transformation from the original rectangle (with vertices A, B, C, D) to the image rectangle (with vertices \(A'\), \(B'\), \(C'\), \(D'\)):

• Check the y - coordinates of corresponding points. For example, point A (let's assume A is at \((-3,1)\)) and \(A'\) is at \((-3, - 3)\). The change in the y - coordinate is \(-3-1=-4\), meaning it moved 4 units down.
• A 180 - degree rotation would change both x and y signs, but here x - coordinates remain the same.
• Reflection over the x - axis would change the sign of the y - coordinate, but the vertical distance here is 4 units (from y = 1 to y=-3, the distance is \(1-(-3) = 4\) units down, not a reflection which would map \((x,y)\) to \((x, - y)\) (e.g., \((-3,1)\) would go to \((-3,-1)\) for reflection over x - axis, not \((-3,-3)\)).
• Dilation would change the size, but the size of the rectangle remains the same.
• Reflection over y - axis changes x - sign, which is not the case here.
• 90 - degree clockwise rotation would change the coordinates in a different way (e.g., \((x,y)\) to \((y, - x)\)), which is not observed.

So the transformation is a translation 4 units down.

Answer:

translation 4 units down