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Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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**4.** **Prompt:** Points **B, C, D, E, F,** and **G** are dilated images of **A** from center **O** with scale factors **2, 3, 4, 5, 6,** and **7**, respectively. Are points **Y, X, W, V, U, T,** and **S** all dilated images of **Z** under the same respective scale factors? Explain why or why not. **Diagram Explanation:** The diagram depicts an origin point labeled as **O**, from which multiple points extend outward, representing dilations at specified scale factors. The points and their respective connections are as follows: - **Z** is a point positioned on the line extending from **O**. - **A** is another point positioned closer to **O** on the same line extending from **O**. - Points **B, C, D, E, F,** and **G** are arranged linearly further from **A** and **O** at respective distances that theoretically correspond to the scale factors: **2, 3, 4, 5, 6,** and **7**. Parallel lines are drawn from corresponding dilation points on **A** to different congruent points on **Z** extending further outward: - **B** is connected to **S** - **C** to **X** - **D** to **W** - **E** to **V** - **F** to **U** - **G** to **T** All these lines emanate from point **O** and extend outward, suggesting that the transformations are based on this center point. **Answer Explanation:** The question seeks to determine if the points **Y, X, W, V, U, T,** and **S** are dilated images of **Z** under the same respective scale factors as for **A** with points **B, C, D, E, F,** and **G**. To verify if the points are dilated images of **Z**, we need to check if the distances between **O** and these points maintain the same ratio as that between **O** and the corresponding points derived from **A**. Essentially: - **S** should be twice the distance from **O** as **Z** is from **O**. - **X** should be three times the distance from **
Transcribed Image Text:**4.** **Prompt:** Points **B, C, D, E, F,** and **G** are dilated images of **A** from center **O** with scale factors **2, 3, 4, 5, 6,** and **7**, respectively. Are points **Y, X, W, V, U, T,** and **S** all dilated images of **Z** under the same respective scale factors? Explain why or why not. **Diagram Explanation:** The diagram depicts an origin point labeled as **O**, from which multiple points extend outward, representing dilations at specified scale factors. The points and their respective connections are as follows: - **Z** is a point positioned on the line extending from **O**. - **A** is another point positioned closer to **O** on the same line extending from **O**. - Points **B, C, D, E, F,** and **G** are arranged linearly further from **A** and **O** at respective distances that theoretically correspond to the scale factors: **2, 3, 4, 5, 6,** and **7**. Parallel lines are drawn from corresponding dilation points on **A** to different congruent points on **Z** extending further outward: - **B** is connected to **S** - **C** to **X** - **D** to **W** - **E** to **V** - **F** to **U** - **G** to **T** All these lines emanate from point **O** and extend outward, suggesting that the transformations are based on this center point. **Answer Explanation:** The question seeks to determine if the points **Y, X, W, V, U, T,** and **S** are dilated images of **Z** under the same respective scale factors as for **A** with points **B, C, D, E, F,** and **G**. To verify if the points are dilated images of **Z**, we need to check if the distances between **O** and these points maintain the same ratio as that between **O** and the corresponding points derived from **A**. Essentially: - **S** should be twice the distance from **O** as **Z** is from **O**. - **X** should be three times the distance from **
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