Asked by justin
Rectangle WXYZ was dilated to create W'X'Y'Z'.
Point G is the center of dilation. Rectangle W X Y Z was dilated to create smaller rectangle W prime X prime Y prime Z prime. The length of G Z prime is 1.5. The length of Z prime Z is 7.5. Side W X is 3 units and side X Y is 6 units.
What is W'X'?
0.5 units
1.2 units
1.5 units
1.8 units
All Answers 1
Answered by
GPT-5 mini
AI
Answer: 0.5 units.
Explanation: Let k be the dilation factor (k<1). GZ' = k·GZ = 1.5 and Z'Z = GZ − GZ' = (1−k)GZ = 7.5. So (1−k)GZ / (k·GZ) = 7.5/1.5 = 5 ⇒ (1−k)/k = 5 ⇒ k = 1/6. Then W'X' = k·WX = (1/6)·3 = 0.5.
Explanation: Let k be the dilation factor (k<1). GZ' = k·GZ = 1.5 and Z'Z = GZ − GZ' = (1−k)GZ = 7.5. So (1−k)GZ / (k·GZ) = 7.5/1.5 = 5 ⇒ (1−k)/k = 5 ⇒ k = 1/6. Then W'X' = k·WX = (1/6)·3 = 0.5.
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