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 RST\triangle RST 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: (x,y)(y,x)(x, y) \to (-y, x) Now apply this rule to each original point:

  1. R(8,2)R(2,8)R(-8, -2) \to R'(\mathbf{2}, \mathbf{-8})
  2. S(1,4)S(4,1)S(1, -4) \to S'(\mathbf{4}, \mathbf{1})
  3. T(2,6)T(6,2)T(-2, -6) \to T'(\mathbf{6}, \mathbf{-2})

Part (b): General Rule

The rotation mapping follows the rule: (x,y)(y,x)(x, y) \to (-y, x)

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:

  1. What is the rule for a 90° clockwise rotation around the origin?
  2. How would the triangle's coordinates change after a 180° rotation about the origin?
  3. What happens to the coordinates of a point after a reflection over the xx-axis?
  4. Can you explain the difference between counterclockwise and clockwise rotations?
  5. 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