Math Problem Statement

Hexagon JKLMNO is rotated 90° clockwise about the origin to produce hexagon J'K'L'M'N'O'. Write the rule for the rotation. (x,y)↦

Solution

When a point (x,y)(x, y) is rotated 90° clockwise about the origin, the transformation rule is:

(x,y)(y,x)(x, y) \mapsto (y, -x)

Thus, the rule for the rotation of hexagon JKLMNO to produce J'K'L'M'N'O' is:

(x,y)(y,x)(x, y) \mapsto (y, -x)

Would you like further explanation or clarification?

Here are 5 related questions to explore this concept:

  1. What would the rule be for a 90° counterclockwise rotation?
  2. How would you rotate a point 180° about the origin?
  3. What effect does a 270° clockwise rotation have on coordinates?
  4. How do you find the new coordinates of a specific vertex after rotation?
  5. What changes if the hexagon is rotated around a point other than the origin?

Tip: Remember, when rotating points, clockwise and counterclockwise rotations produce different transformations!

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Math Problem Analysis

Mathematical Concepts

Geometry
Rotations
Transformations

Formulas

(x, y) ↦ (y, -x) for 90° clockwise rotation

Theorems

Rotation theorem about the origin

Suitable Grade Level

Grades 8-10