Math Problem Statement
Solution
The problem shown in the image asks to rotate triangle by 270° counterclockwise around the origin. Let's break down how to approach this type of transformation:
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Rotation of points 270° counterclockwise:
- The general rule for a 270° counterclockwise rotation around the origin is to switch the coordinates of each point and negate the new first coordinate.
- For a point , the transformation is:
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Applying the rule to each vertex of the triangle:
- Assume the coordinates of , , and are , , and . Based on the diagram, these points will be rotated using the rule .
- After the transformation, the new coordinates of , , and will be plotted on the graph.
Would you like me to calculate the new coordinates of the points , , and from the diagram? Let me know if you need more details on any specific part of the process!
Further Questions to Explore:
- What is the rule for a 90° counterclockwise rotation around the origin?
- How does the rotation affect the orientation of the shape?
- What happens to a shape's size and angles during rotation?
- How can you verify the accuracy of a transformation on a graph?
- How does the triangle's image differ after a reflection instead of a rotation?
Tip: Always remember the origin is the fixed point during any rotation unless stated otherwise.
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Transformations
Rotations
Formulas
Rotation Formula for 270°: (x, y) → (y, -x)
Theorems
Rotation Theorem around Origin
Suitable Grade Level
Grades 7-9
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