Question

NEED IMMEDIATE HELP 10 POINTS

According to these three facts, which statements are true? Circle D has center of (2,3) and radius 7. Circle F is a translation of circle D, 2 units right. Circle F is a dilation of circle D with a scale factor of 4. Select each correct answer.

1. The center of circle F is (0,3)
2. Circle F and circle D are congruent
3. The radius of circle F is 28
4. Circle F and circle D are similar

Answer 1

Explanation:

you made some confusing typos.

is circle F the result of the translation, or of the dilation ?

I assume the translation result is called circle E.

and the dilation result is truly circle F. but I will check both cases for each statement.

1. is false (in both cases).

because the dilation would change the size of the circle, but keep it in the same place. so the coordinates of the center of F are the same as for the center of circle D.

and for the translation 2 units to the right it is wrong, because to the right means the x-coordinate increases. the center of the translated circle would be (2+2, 3) = (4,3).

2. is false (for the dilation case).

because F has a different size than D, they cannot be congruent (they really must be able to cover each other up with nothing overlapping in any direction).

but it would be true for the translation case. in a translation the original shape and size stays the same, only the location changes. so, yes, they would be congruent.

3. this is true (for the dilation case).

all distances in a shape change by the scaling factor. so, also the radius in the circle. 7×4 = 28.

for the translation case this is false, of course, as shadow and size remains unchanged.

4. this is true (in both cases).

to be similar there has to be a common scaling factor between them for all distances inside the shapes.

that scaling factor is 4 in the dilation case and 1 in the translation case.