Math Problem Statement
Solution
To solve this problem, we will break it into two transformations as specified:
- Reflection across the line .
- Rotation 180° counterclockwise around the origin.
Step 1: Reflection across the line
We need to reflect the coordinates of points , , and across the horizontal line .
- The formula for reflecting a point across a horizontal line is: In this case, .
Step 2: 180° Rotation Counterclockwise Around the Origin
After reflection, we will rotate the new points 180° counterclockwise around the origin. The formula for rotating a point by 180° counterclockwise is:
Let me now apply these transformations to the triangle's points and plot the resulting image.
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Math Problem Analysis
Mathematical Concepts
Geometric Transformations
Reflections
Rotations
Formulas
Reflection formula across a horizontal line y = k: (x', y') = (x, 2k - y)
Rotation formula for 180° counterclockwise: (x', y') = (-x, -y)
Theorems
Geometric Transformation Theorems
Suitable Grade Level
Grades 8-10
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