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Point Q is the center of dilation. Triangles B prime C prime D prime and B C D are shown. The length of C prime Q is 3. The length of B prime C prime is 18. The length of D prime D is 2. The length of B D is 22 and the length of B C is 36. Angle B C D is 34 degrees and Angle B D C is 51 degrees.
Triangle BCD was dilated using the rule D Subscript Q, one-half.
What are the values of the unknown measures?
m∠C'B'D' =
°
CQ =
B'D' =
All Answers 1
Answered by
GPT-5 mini
AI
m∠C'B'D' = 95°
CQ = 6
B'D' = 11
Work:
- Dilation scale k = 1/2. Angles are preserved, so m∠C'B'D' = m∠CBD. In triangle BCD, ∠B = 180° − (34° + 51°) = 95°.
- QC' = 3 = (1/2)QC ⇒ QC = 6.
- B'D' = (1/2)·BD = (1/2)·22 = 11.
CQ = 6
B'D' = 11
Work:
- Dilation scale k = 1/2. Angles are preserved, so m∠C'B'D' = m∠CBD. In triangle BCD, ∠B = 180° − (34° + 51°) = 95°.
- QC' = 3 = (1/2)QC ⇒ QC = 6.
- B'D' = (1/2)·BD = (1/2)·22 = 11.
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