Math Problem Statement

Graph the image of square PQRS after a rotation 90° clockwise around the origin.

Solution

To solve this problem, we need to find the new coordinates of square PQRS after rotating it 90° clockwise around the origin. For a 90° clockwise rotation, the transformation of a point (x,y)(x, y) becomes (y,x)(y, -x).

Let’s determine the coordinates of the points first:

  • P=(4,2)P = (4, 2)
  • Q=(8,2)Q = (8, 2)
  • R=(8,6)R = (8, 6)
  • S=(4,6)S = (4, 6)

Now, applying the rotation rule (x,y)(y,x)(x, y) \to (y, -x):

  1. Point P (4, 2) becomes (2,4)(2, -4)
  2. Point Q (8, 2) becomes (2,8)(2, -8)
  3. Point R (8, 6) becomes (6,8)(6, -8)
  4. Point S (4, 6) becomes (6,4)(6, -4)

The new coordinates of the rotated square will be:

  • P=(2,4)P' = (2, -4)
  • Q=(2,8)Q' = (2, -8)
  • R=(6,8)R' = (6, -8)
  • S=(6,4)S' = (6, -4)

You can now plot these points on the graph and connect them to form the image of the square after the 90° clockwise rotation.

Do you want further clarification or details on how I got these points?

Here are 5 related questions to expand your understanding:

  1. What is the rule for a 90° counterclockwise rotation?
  2. How do you perform a 180° rotation around the origin?
  3. What are other common transformations besides rotation?
  4. Can this same method be applied to non-square shapes?
  5. How would the result change if we rotated by 270° clockwise instead?

Tip: Always remember to apply the transformation rules carefully, paying attention to signs and coordinate swapping during rotations.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Rotation
Transformations

Formulas

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

Theorems

Rotation Theorem

Suitable Grade Level

Grades 8-10