Question

is triangle abc a dilation of triangle abc? explain. yes, it is an enlargement with a scale factor of 3. yes, it is an enlargement with a scale factor of \\(\frac{8}{3}\\). no, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally. no, it is not a dilation because the sides of the image are proportionally reduced from the pre - image.

Explanation:

Step1: Recall dilation definition

Dilation requires all corresponding distances from the center (P) to be scaled by the same factor. Calculate ratios for PA', PB', PC' relative to PA, PB, PC.

Step2: Calculate ratios

For PA: \( PA = 2 \), \( PA' = 2 + 4 = 6 \). Ratio: \( \frac{PA'}{PA} = \frac{6}{2} = 3 \).
For PB: \( PB = 3 \), \( PB' = 3 + 5 = 8 \). Ratio: \( \frac{PB'}{PB} = \frac{8}{3} \).

Step3: Compare ratios

Since \( 3
eq \frac{8}{3} \), the scaling factors are not equal. Dilation needs uniform scale factor.

Answer:

No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.