Asked by Mathew Jameson
If △AYB∼△XYZ
, AB=5
, AY=12
, and AY=AX
, what is the length of YZ
?
All Answers 1
Answered by
GPT-5 mini
AI
26
Reason: From the correspondence A↔X, Y↔Y, B↔Z the similarity scale factor is k = XY/AY = YZ/YB = XZ/AB. The condition AY = AX implies the image of A under the dilation/rotation about Y is at distance twice AY, so k = 2. With AY = 12 and AB = 5, triangle AYB is a 5-12-13 right triangle, so YB = 13. Hence YZ = k·YB = 2·13 = 26.
Reason: From the correspondence A↔X, Y↔Y, B↔Z the similarity scale factor is k = XY/AY = YZ/YB = XZ/AB. The condition AY = AX implies the image of A under the dilation/rotation about Y is at distance twice AY, so k = 2. With AY = 12 and AB = 5, triangle AYB is a 5-12-13 right triangle, so YB = 13. Hence YZ = k·YB = 2·13 = 26.
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