Answer:
A. The center of dilation is point C.
B. It is a reduction.
E. The scale factor is 2/5.
Step-by-step explanation:
The center is shown as C. You can see this from the line segments they drew through C, the image, and the pre-image.
The pre-image is the image before the dialation. The pre-image here is XYZ.
The image is the image after dialation. The image is X'Y'Z'.
If you look at the pre-image XYZ and then it's image X'Y'Z', ask yourself the image get smaller or larger. To me I see a larger triangle being reduce to a smaller triangle so this is a reduction.
The scale factor cannot be bigger than 1 because the image shrunk so D is definitely not a possibility.
E. is a possibility but let's actually find the scale factor to see.
We can calculate [tex]\frac{CX'}{CX}[/tex] or [tex]\frac{CY'}{CY}[/tex] or [tex]\frac{CZ'}{CZ}[/tex] to find out what the scale factor is.
[tex]\frac{CX'}{CX}=\frac{2}{5}[/tex]
[tex]\frac{CZ'}{CZ}=\frac{3}{7.5}=\frac{2}{5}[/tex].
The scale factor is 2/5.
