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¯¯¯¯¯¯¯¯
?(7 points)
Responses
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).
C' is at (9,-18) and D' is at (18,-9).
C' is at (2,-1) and D' is at (1,-2).
C' is at (2,-1) and D' is at (1,-2).
The length of C′D′¯¯¯¯¯¯¯¯¯¯¯
is approximately 4.24 units.
The length of line segment cap c prime cap d prime is approximately 4.24 units.
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¯¯¯¯¯¯¯¯
?(7 points)
Responses
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).
C' is at (9,-18) and D' is at (18,-9).
C' is at (2,-1) and D' is at (1,-2).
C' is at (2,-1) and D' is at (1,-2).
The length of C′D′¯¯¯¯¯¯¯¯¯¯¯
is approximately 4.24 units.
The length of line segment cap c prime cap d prime is approximately 4.24 units.
Answers
Answered by
GPT-4o mini
To prove that the dilation of a line segment \( CD \) with a scale factor of 13 and a center of dilation at the origin results in a line segment that is 13 times the length of \( CD \), the relevant fact is that the lengths of the dilated segment should be based on the scale factor.
For this particular proof, the statement regarding the length of the original segment \( C'D' \) before dilation is crucial. The proof should start by establishing the length of the segment \( C'D' \) before the dilation, which is often necessary to confirm that when you apply a dilation factor, the new length will indeed be scaled appropriately.
Given the responses:
1. "The length of C′D′ is approximately 1.41 units."
2. "The length of line segment cap c prime cap d prime is approximately 1.41 units."
3. "C' is at (9,-18) and D' is at (18,-9)."
4. "C' is at (2,-1) and D' is at (1,-2)."
5. "The length of C′D′ is approximately 4.24 units."
6. "The length of line segment cap c prime cap d prime is approximately 4.24 units."
The correct statement to include in the proof, regarding the length of the original segment before dilation, would be:
**"The length of C′D′ is approximately 4.24 units."**
or
**"The length of line segment cap c prime cap d prime is approximately 4.24 units."**
This indicates that after applying the scale factor of 13, the new length of the segment would be \( 13 \times 4.24 \) units. This logical thread would help in establishing that the dilation indeed results in a segment length that is 13 times that of \( CD \).
Thus, you may select either of the fifth or sixth statements for your proof.
For this particular proof, the statement regarding the length of the original segment \( C'D' \) before dilation is crucial. The proof should start by establishing the length of the segment \( C'D' \) before the dilation, which is often necessary to confirm that when you apply a dilation factor, the new length will indeed be scaled appropriately.
Given the responses:
1. "The length of C′D′ is approximately 1.41 units."
2. "The length of line segment cap c prime cap d prime is approximately 1.41 units."
3. "C' is at (9,-18) and D' is at (18,-9)."
4. "C' is at (2,-1) and D' is at (1,-2)."
5. "The length of C′D′ is approximately 4.24 units."
6. "The length of line segment cap c prime cap d prime is approximately 4.24 units."
The correct statement to include in the proof, regarding the length of the original segment before dilation, would be:
**"The length of C′D′ is approximately 4.24 units."**
or
**"The length of line segment cap c prime cap d prime is approximately 4.24 units."**
This indicates that after applying the scale factor of 13, the new length of the segment would be \( 13 \times 4.24 \) units. This logical thread would help in establishing that the dilation indeed results in a segment length that is 13 times that of \( CD \).
Thus, you may select either of the fifth or sixth statements for your proof.
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