Question

1. (03.01 hc)

quadrilateral efgh was dilated by a scale factor of 2 from the center (1, 0) to create efgh.
which characteristic of dilations compares segment ef to segment ef? (1 point)
a segment that passes through the center of dilation in the pre - image continues to pass through the center of dilation in the image.
a segment in the image has the same length as its corresponding segment in the pre - image.
a segment that passes through the center of dilation in the pre - image does not pass through the center of dilation in the image.
a segment in the image is proportionally longer or shorter than its corresponding segment in the pre - image.

1. (03.01 mc)

Explanation:

Step1: Recall the properties of dilation

Dilation is a transformation that changes the size of a figure. The scale factor determines if the figure is enlarged (scale factor > 1) or reduced (scale factor < 1).

Step2: Analyze each option

• Option 1: Segment \(EF\) and \(E'F'\) do not pass through the center of dilation \((1,0)\), so this property is not relevant here.
• Option 2: Since the scale factor is \(2\), the lengths of corresponding segments are not the same.
• Option 3: This is a false statement about dilation. If a segment passes through the center of dilation in the pre - image, it passes through the center in the image. But again, \(EF\) and \(E'F'\) do not pass through the center.
• Option 4: Given the scale factor \(k = 2\), if the length of segment \(EF\) is \(l\), the length of segment \(E'F'\) is \(kl\). So a segment in the image (\(E'F'\)) is proportionally longer (because \(k=2> 1\)) than its corresponding segment (\(EF\)) in the pre - image.

Answer:

D. A segment in the image is proportionally longer or shorter than its corresponding segment in the pre - image.