Math Problem Statement
Triangle RST is rotated 90° counterclockwise about the origin. The result is triangle R'S'T'. Determine the final coordinates after the rotation and the general rule for the transformation.
Solution
Solution to the Given Problem:
The question involves rotating the triangle 90° counterclockwise about the origin. Here's how to solve each part:
Part (a): Coordinates After the Rotation
The general rule for a 90° counterclockwise rotation around the origin is: Now apply this rule to each original point:
Part (b): General Rule
The rotation mapping follows the rule:
Thus, the correct answer is the third option.
Let me know if you'd like further clarification on the calculations or additional help!
5 Related Questions:
- What is the rule for a 90° clockwise rotation around the origin?
- How would the triangle's coordinates change after a 180° rotation about the origin?
- What happens to the coordinates of a point after a reflection over the -axis?
- Can you explain the difference between counterclockwise and clockwise rotations?
- How can we graphically verify a transformation on a coordinate plane?
Tip:
Always remember to double-check your transformations by plotting both the original and transformed points to ensure accuracy!
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Rotations in the Coordinate Plane
Transformations
Formulas
(x, y) → (-y, x) for a 90° counterclockwise rotation
Theorems
Rotation transformation rules
Suitable Grade Level
Grades 8-10