Math Problem Statement

Graph the preimage and image of each rotation. Determine the coordinates of D'.

Solution

The image shows a rotation task where you're asked to determine the coordinates of point D' after a 90° rotation. The original coordinates of D are given as D(5,1)D(5, -1).

90° Rotation Rule:

  • Clockwise: The rule for a 90° clockwise rotation around the origin is (x,y)(y,x)(x, y) \to (y, -x).
  • Counterclockwise: The rule for a 90° counterclockwise rotation is (x,y)(y,x)(x, y) \to (-y, x).

Since the image doesn't specify the direction, I will assume it's counterclockwise, which is most common unless otherwise stated.

Applying the 90° Counterclockwise Rotation to D(5,1)D(5, -1):

Using the rule (x,y)(y,x)(x, y) \to (-y, x), we get:

  • D(5,1)D((1),5)=D(1,5)D(5, -1) \to D'(-(-1), 5) = D'(1, 5).

Thus, the coordinates of DD' are (1,5)\boxed{(1, 5)}, matching the third option.

Would you like more details, or do you have any questions?

Here are 5 related questions:

  1. How would the coordinates change if the rotation was 90° clockwise?
  2. What is the effect of a 180° rotation on any point?
  3. How do you rotate a point 270° counterclockwise?
  4. Can you apply the rotation rule to point A(4, -1)?
  5. How does the distance from the origin affect the result of a rotation?

Tip: When rotating points, always pay attention to the direction and whether the rotation is around the origin or another point.

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Math Problem Analysis

Mathematical Concepts

Geometry
Coordinate Geometry
Rotations

Formulas

90° Counterclockwise Rotation: (x, y) → (-y, x)
90° Clockwise Rotation: (x, y) → (y, -x)

Theorems

Rotation Theorem in Geometry

Suitable Grade Level

Grades 8-10