QQuestionMathematics
QuestionMathematics
As shown in the graph below, the quadrilateral is a rectangle. Which transformation would not map the rectangle onto itself?
A reflection over the x-axis
A reflection over the line x= 4
A rotation of 180° about the origin
A rotation of 180° about the point (4,0)
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the Rectangle's Properties
- The rectangle appears to have vertices at (0,0), (8,0), (8,4), and (0,4) - The width is 8 units - The height is 4 units - The center of the rectangle is at the point (4,2)
Step 3:: Analyze Reflection over x-axis
- This reflection would map (x,y) to (x,-y) - The vertices would become (0,0), (8,0), (8,- 4), and (0,- 4) - This DOES NOT map the rectangle onto itself
Step 4:: Analyze Reflection over x = 4
- This reflection would map (x,y) to (8 -x,y) - The vertices would become (8,0), (0,0), (0,4), and (8,4) - This DOES map the rectangle onto itself
Step 5:: Rotation 180° about Origin
- This rotation maps (x,y) to (-x,-y) - The vertices would become (0,0), (- 8,0), (- 8,- 4), and (0,- 4) - This DOES map the rectangle onto itself
Step 6:: Rotation 180° about (4,0)
- This rotation maps (x,y) to (8 -x,-y) - The vertices would become (8,0), (0,0), (0,- 4), and (8,- 4) - This DOES map the rectangle onto itself
Final Answer
A reflection over the x-axis would NOT map the rectangle onto itself.
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