29 POINTS! ANSWER ASAP PLEASE. Which statements about the dilation are true? Check all that apply. (multiple choice question) (image provided below)A. The center of dilation is point CB. It is a reductionC. It is an enlargementD. The scale factor is 2.5E. The scale factor is 2/5

Accepted Solution

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.