Question

a transformation of rectangle abcd results in rectangle abcd. which transformation maps the pre - image to the image? dilation reflection rotation translation

Explanation:

To determine the transformation, we analyze each option:

• Dilation: It changes the size of a figure. The pre - image rectangle \(ABCD\) has length \(AB = 5\) and height \(BC=4\), and the image rectangle \(A'B'C'D'\) has length \(A'B' = 10\) and height \(B'C' = 8\). We can see that the scale factor for the length is \(\frac{10}{5}=2\) and for the height is \(\frac{8}{4} = 2\). So the figure is enlarged by a scale factor of 2, which is a dilation.
• Reflection: A reflection would flip the figure over a line, but there is no indication of a flip here as the shape and orientation (relative to the enlargement) don't suggest a reflection.
• Rotation: A rotation would turn the figure around a point, but the figure is just enlarged, not rotated.
• Translation: A translation would move the figure without changing its size or shape, but here the size has changed.

Answer:

dilation