Question

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

Explanation:

Step1: Recall Dilation Definition

Dilation requires scale factor (ratio of image to pre - image distances from center) to be constant.

Step2: Calculate Ratios

For point A: \(PA = 2\), \(PA'=4\), ratio \(=\frac{4}{2}=2\). For point B: \(PB = 3\), \(PB' = 5\), ratio \(=\frac{5}{3}\). These ratios are not equal.

Step3: Analyze Options

• First option: Wrong, dilation can reduce (if scale factor < 1), but here ratios are not constant.
• Second option: Correct, because the ratios of distances from center (P) for A and B are not equal (\(2

eq\frac{5}{3}\)), so points are not moved proportionally.

• Third option: Wrong, scale factor is not constant (\(\frac{4}{2}=2

eq\frac{5}{3}\)).

• Fourth option: Wrong, scale factor is not 3 (e.g., for B, \(\frac{5}{3}

eq3\)).

Answer:

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