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問題

解法ステップ

1. Understand the question

   what sequence of transformations will map a triangle from (1,1), (3,1), and (2,4) to (-1,-1), (-3,-1), and (-2,-4)?

   a. reflection over the y-axis

   b. dilation by 0.5, reflection over the y-axis

   c. rotation 180 degrees

   d. translation 3 units right, reflection over y-axis

2. Explanation

   Step1: Analyze coordinate transformation

   Compare original points $(x,y)$ to new points $(-x,-y)$:

   • $(1,1) \to (-1,-1)$, $(3,1) \to (-3,-1)$, $(2,4) \to (-2,-4)$

   Step2: Match to transformation rule

   A 180° rotation about the origin follows the rule $(x,y) \to (-x,-y)$, which matches the coordinate change.

   Step3: Eliminate other options

   • Reflection over y-axis: $(x,y) \to (-x,y)$ (does not match $-y$)
   • Dilation + y-axis reflection: Scales coordinates first, does not result in $(-x,-y)$
   • Translation + y-axis reflection: Shifts coordinates first, does not result in $(-x,-y)$
3. Final answer

   c. Rotation 180 degrees

答え

Question Analysis

OCR Text

what sequence of transformations will map a triangle from (1,1), (3,1), and (2,4) to (-1,-1), (-3,-1), and (-2,-4)?

a. reflection over the y-axis

b. dilation by 0.5, reflection over the y-axis

c. rotation 180 degrees

d. translation 3 units right, reflection over y-axis

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