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 properties

Dilation requires that the ratio of distances from the center of dilation (point \( P \)) to corresponding points of the image and pre - image is constant (scale factor).

Step2: Calculate ratios for \( PA, PA' \) and \( PB, PB' \)

For \( PA \) and \( PA' \): \( PA = 2 \), \( PA'=2 + 4=6 \). The ratio \( \frac{PA'}{PA}=\frac{6}{2} = 3 \).
For \( PB \) and \( PB' \): \( PB = 3 \), \( PB'=3 + 5 = 8 \). The ratio \( \frac{PB'}{PB}=\frac{8}{3}
eq3 \).
Since the ratios are not equal, the points of the image are not moved away from the center of dilation proportionally. So, triangle \( A'B'C' \) is not a dilation of triangle \( ABC \) because the proportionality condition for dilation is not met.

Answer:

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