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题目

解题步骤

1. Understand the question

   Turn 1 Question

   which sequence of transformations maps a rectangle from (1,2), (1,4), (3,4), and (3,2) to (-2,-4), (-2,-8), (-6,-8), and (-6,-4)?

   a. translation by 9 units left and 12 units down
   b. translation by 2 units right
   c. dilation by scale factor of -2
   d. dilation by scale factor of 2

   Turn 2 Question

   Which transformation does not preserve the size of a figure? a. Reflection b. Rotation c. Dilation d. Translation

2. Response

   Turn 1 Answer

3. Explanation

   Step1: Pick a reference point

   Take the point $(1,2)$ and its image $(-2,-4)$.

   Step2: Test dilation factor

   Check scaling: $1 \times k = -2$ and $2 \times k = -4$. Solve for $k$: $k = \frac{-2}{1} = -2$, $k = \frac{-4}{2} = -2$.

   Step3: Verify with another point

   Test $(1,4)$: $1 \times (-2) = -2$, $4 \times (-2) = -8$, which matches $(-2,-8)$.

   Step4: Eliminate other options

   Translation would add/subtract constants, not scale coordinates. Scale factor 2 would give positive values, not negative.

4. Brief Explanations

   Reflections, rotations, and translations are rigid transformations—they only change the position or orientation of a figure, keeping its side lengths, angles, and overall size identical. Dilation involves scaling a figure by a factor (other than 1), which increases or decreases its linear dimensions, thus changing its size.

5. Final answer

   c. dilation by scale factor of -2

   Turn 2 Answer

答案

Question Analysis

OCR Text

Which transformation does not preserve the size of a figure? a. Reflection b. Rotation c. Dilation d. Translation

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