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.
(diagram includes points p, a, a (pa=2, aa=4), p, b, b (pb=3, bb=5), and c, c on a horizontal line from p)

Explanation:

Step1: Recall Dilation Definition

Dilation requires that the ratio of distances from the center of dilation (point \( P \)) to corresponding points (e.g., \( PA'/PA \), \( PB'/PB \), \( PC'/PC \)) is constant (scale factor).

Step2: Calculate Ratios

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

Step3: Compare Ratios

Since \( 3
eq \frac{8}{3} \), the distances from \( P \) to corresponding vertices are not proportional. Thus, it is not a dilation.

Answer:

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