Question

Point P is the center of dilation. Triangle S T U is dilated to create triangle S prime T prime U prime. The length of P T is 2. The length of T T prime is 10.
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, One-sixth, 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.

Answer 1

Answers:
- The triangle pre-image is closer to the point of dilation than the image.
- The value of the scale factor, 6, is greater than 1.

Reason: PT' = PT + TT' = 2 + 10 = 12, so scale factor k = PT'/PT = 12/2 = 6 (>1), so the image is farther from P (an enlargement).