Question

what steps would you take to determine if these figures are similar? check all that apply. use a scale factor of 2. multiply the vertices of polygon abcd by \\(\frac{1}{2}\\). translate the intermediate image 4 units down. perform two different dilations. reflect the intermediate image.

Explanation:

To determine if the figures are similar, we analyze each option:

• Use a scale factor of 2: The smaller figure is not twice the size of the larger one, so this is incorrect.
• Multiply vertices of \(ABCD\) by \(\frac{1}{2}\): Dilation with scale factor \(\frac{1}{2}\) reduces the larger trapezoid \(ABCD\) to a smaller size, matching the relative proportions of \(A''B''C''D''\). This is a valid step.
• Translate intermediate image 4 units down: After dilating \(ABCD\) by \(\frac{1}{2}\), translating the result 4 units down aligns it with \(A''B''C''D''\). This is valid.
• Perform two different dilations: Only one dilation (scale factor \(\frac{1}{2}\)) is needed, so this is incorrect.
• Reflect the intermediate image: The figures are not reflections of each other, so this is incorrect.

Answer:

• Multiply the vertices of polygon \(ABCD\) by \(\frac{1}{2}\)
• Translate the intermediate image 4 units down