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問題

解法ステップ

1. Understand the question

   Turn 1 Question

   which transformation would you apply to map a rectangle at (1,1), (1,3), (3,3), and (3,1) to (4,5), (4,7), (6,7), and (6,5)?
   a. dilation by a scale factor of 2
   b. translation 3 units right and 4 units up
   c. rotation 90 degrees clockwise
   d. reflection over the x-axis

   Turn 2 Question

   What does a dilation transformation do to a figure? a. Resizes it while maintaining its shape. b. Turns it around a point. c. Flips it over a line. d. Slides it in any direction.

   Turn 3 Question

   Which of the following transformations would you use to make a figure smaller while keeping the same proportions? a. Dilation by a scale factor of 0.5 b. Reflection over the x-axis c. Rotation 180 degrees d. Translation left and up

2. Response

   Turn 1 Answer

3. Explanation

   Step1: Compare x-coordinates

   Take original point $(1,1)$ and new point $(4,5)$:
   $4 - 1 = 3$
   Check another pair: $(1,3)$ to $(4,7)$:
   $4 - 1 = 3$

   Step2: Compare y-coordinates

   Take original point $(1,1)$ and new point $(4,5)$:
   $5 - 1 = 4$
   Check another pair: $(3,3)$ to $(6,7)$:
   $7 - 3 = 4$

   Step3: Verify transformation

   All original x-values increase by 3 (right 3 units), all original y-values increase by 4 (up 4 units). This matches translation.

4. Brief Explanations

   Each option corresponds to a different transformation: rotation turns a figure around a point, reflection flips it over a line, translation slides it, while dilation changes the figure's size proportionally without altering its shape.

5. Brief Explanations

   Dilation changes a figure's size while preserving proportions; a scale factor between 0 and 1 reduces the figure. Reflection, rotation, and translation only change the figure's position/orientation, not its size.

6. Final answer

   b. Translation 3 units right and 4 units up

   Turn 2 Answer

答え

Question Analysis

OCR Text

Which of the following transformations would you use to make a figure smaller while keeping the same proportions? a. Dilation by a scale factor of 0.5 b. Reflection over the x-axis c. Rotation 180 degrees d. Translation left and up

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