Math Problem Statement

Here is triangle ABC. Draw the new image of triangle ABC after a rotation of 120° clockwise around point B. Shade the new image and label it A'B'C'.

Solution

This task involves rotating triangle ABCABC 120° clockwise around point BB. Let's break down the steps to perform the rotation:

  1. Rotation around point B: Since BB is the center of rotation, it will remain fixed in its current position. Only points AA and CC will move during the 120° clockwise rotation.

  2. 120° clockwise rotation steps:

    • For each point (AA and CC), measure the distance from BB, and then rotate this vector by 120° clockwise.
    • The new positions of AA' and CC' can be plotted on the grid, keeping their distance from BB the same as the original.
  3. Labeling: After the rotation, you will label the new triangle as ABCA'B'C', and shade this new triangle.

Would you like a detailed explanation on how to manually rotate points using a coordinate system, or should I assist with a more specific step from this? Let me know if you want to dive into any specific details of the process.

Here are 5 related questions:

  1. How do you find the coordinates of points after rotation?
  2. What are other rotation angles, and how would they affect the figure?
  3. How can you verify if a rotation was performed correctly?
  4. What happens when rotating a shape around a point not on the shape itself?
  5. How would a counterclockwise rotation differ from a clockwise one?

Tip: When rotating figures, use tracing paper to align the shape before and after rotation to visualize the transformation easily!

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Math Problem Analysis

Mathematical Concepts

Geometry
Transformations
Rotations

Formulas

Rotation formula: (x', y') = (x*cos(θ) - y*sin(θ), x*sin(θ) + y*cos(θ))
Clockwise rotation for 120°

Theorems

Rotation transformation theorem
Properties of rotations

Suitable Grade Level

Grades 7-10