Which statement is part of the proof that the dilation of CD¯¯¯¯¯¯¯¯

Question

Which statement is part of the proof that the dilation of  CD¯¯¯¯¯¯¯¯
  with a scale factor of  13
  and a center of dilation at the origin will result in a line segment that is  13
  the length of  CD¯¯¯¯¯¯¯¯
 ?

(1 point)
Responses

C′
 is at (2,−1)
 and D′
 is at (1,−2)
.
upper C prime  is at  open paren 2 comma negative 1 close paren  and  upper D prime  is at  left parenthesis 1 comma negative 2 right parenthesis .

The length of C′D′¯¯¯¯¯¯¯¯¯¯¯
 is approximately 4.24.
The length of  line segment cap c prime cap d prime is approximately 4.24.

The length of C′D′¯¯¯¯¯¯¯¯¯¯¯
 is approximately 1.41 units.
The length of  line segment cap c prime cap d prime  is approximately 1.41 units.

C′
 is at (9,−18)
 and D′
 is at (18,−9

GPT-4o mini · Answer

The statement that best fits as part of the proof for the dilation of line segment \( CD \) with a scale factor of \( 13 \) is:

C′ is at (2,−1) and D′ is at (1,−2).

This statement indicates the new positions of the points after dilation.

However, for the dilation resulting in the new segment being \( 13 \) times the length of \( CD \), the points after dilation would need to reflect that. If the original segment \( CD \) has a specific length, after the dilation, the new segment \( C'D' \) should appropriately reflect the length increase per the given scale factor of \( 13 \).

Ultimately, if you're looking for the result after applying the dilation, a confirming statement about the length of \( C'D' \) being \( 13 \) times the original length of \( CD \) would also be an appropriate part of that process. If none of the lengths provided are accurate or if those points are incorrect, the provided coordinates do not mathematically conform to a dilation by a scale factor of \( 13 \).

For a rigorous proof, you would typically establish that the length of segment \( C'D' \) is indeed \( 13 \) times the length of \( CD \). If the coordinates and lengths given require more clarification or specific mathematical validation, please provide the original coordinates of \( C \) and \( D \) for a complete assessment.