Question

which statements justify that the dilation of triangle stu is an enlargement increasing its size by the magnitude of the scale factor? select two options. the triangle pre - image is closer to the point of dilation than the image. the triangle image is closer to the point of dilation than the pre - image. the value of the scale factor, \\( \frac{1}{6} \\), is between 0 and 1. the value of the scale factor, 6, is greater than 1. the vertices of the pre - image are collinear with the vertices of the image.

Explanation:

Step1: Analyze the distance from pre - image and image to the center of dilation

In a dilation, if it is an enlargement, the pre - image is closer to the center of dilation (point \(P\)) than the image.

Step2: Analyze the scale factor

If the scale factor \(k> 1\), the dilation is an enlargement. Here, if we assume the scale factor is calculated as \(\frac{PT'}{PT}\) (where \(PT = 2\) and \(PT'=10\), the scale factor \(k = 5\) in terms of the ratio of lengths from the center of dilation. In general, for an enlargement, the scale factor \(k>1\). Also, for a dilation, the pre - image and image have collinear vertices with the center of dilation, but this property does not distinguish between enlargement and reduction.

Answer:

The triangle pre - image is closer to the point of dilation than the image. The value of the scale factor, \(6\) (assuming correct scale factor calculation based on lengths from center of dilation, if \(PT = 2\) and \(PT'=12\) scale factor \(k = 6\)), is greater than \(1\). So the two options are: "The triangle pre - image is closer to the point of dilation than the image" and "The value of the scale factor, \(6\), is greater than \(1\)"