Math Problem Statement
What is the image of the point left parenthesis, minus, 4, comma, 8, right parenthesis(−4,8) after a rotation of 90, degrees90∘ counterclockwise about the origin?
Solution
To find the image of the point after a 90° counterclockwise rotation about the origin, we use the rotation formula:
Rotation Formula
For a 90° counterclockwise rotation about the origin, a point is transformed to .
Applying the Formula
Given the point :
The new coordinates after a 90° counterclockwise rotation will be:
Substitute and :
Conclusion
The image of the point after a 90° counterclockwise rotation about the origin is .
Would you like more details on this or have any questions?
Here are 5 related questions to further explore this concept:
- What is the image of the point after a 90° counterclockwise rotation about the origin?
- How would you describe a 270° clockwise rotation's effect on a point's coordinates?
- What is the result of rotating a point by 180° about the origin?
- How does the distance from the origin change after rotating a point 90° counterclockwise?
- Can you find the image of a point after a 360° rotation about the origin?
Tip: Remember that a 90° counterclockwise rotation changes the sign of the y-coordinate and swaps the coordinates.
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Rotations
Formulas
Rotation formula for 90° counterclockwise rotation about the origin
Theorems
-
Suitable Grade Level
Grades 9-12
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