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: Calculate the scale factor for \(PA\) and \(PA'\)

For segment \(PA\), \(PA = 2\), and for segment \(PA'\), \(PA'=2 + 4=6\). The ratio \(\frac{PA'}{PA}=\frac{6}{2} = 3\).

Step2: Calculate the scale factor for \(PB\) and \(PB'\)

For segment \(PB\), \(PB = 3\), and for segment \(PB'\), \(PB'=3 + 5 = 8\). The ratio \(\frac{PB'}{PB}=\frac{8}{3}\).

Step3: Check the proportionality

Since \(\frac{PA'}{PA}
eq\frac{PB'}{PB}\) (i.e., \(3
eq\frac{8}{3}\)), the points of the image \(A'B'C'\) are not moved away from the center of dilation \(P\) proportionally. So, it is not a dilation.

Answer:

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