https://file.aiquickdraw.com/mathbot/file/1731947196860b1dd53nb.jpg

The image contains two geometry tasks involving transformations on the coordinate plane. Here's how to solve each part:

---

### Task 4:
- **Vertices of Triangle ABC**:
  - \( A(3,3) \)
  - \( B(1,3) \)
  - \( C(2,1) \)

- **Steps**:
  1. **Graph the Triangle ABC**: Plot the points \( A(3,3) \), \( B(1,3) \), and \( C(2,1) \) on the coordinate plane and connect them to form a triangle.
  2. **Rotate 90 Degrees Clockwise About the Origin**:
     - The rule for rotating a point 90° clockwise is:
       \[
       (x, y) \to (y, -x)
       \]
     - Applying the rule:
       - \( A(3,3) \to A'(3,-3) \)
       - \( B(1,3) \to B'(3,-1) \)
       - \( C(2,1) \to C'(1,-2) \)
  3. **Graph the New Triangle \( A'B'C' \)**: Plot \( A'(3,-3) \), \( B'(3,-1) \), and \( C'(1,-2) \) and connect them.
  4. **Write the Rule**: The rule for this rotation is \( (x, y) \to (y, -x) \).

---

### Task 5:
- **Vertices of Triangle ABC**:
  - \( A(-2,0) \)
  - \( B(0,3) \)
  - \( C(2,2) \)

- **Steps**:
  1. **Graph the Triangle ABC**: Plot \( A(-2,0) \), \( B(0,3) \), and \( C(2,2) \) on the coordinate plane and connect them to form a triangle.
  2. **Reflect Over the y-Axis**:
     - The rule for reflecting over the y-axis is:
       \[
       (x, y) \to (-x, y)
       \]
     - Applying the rule:
       - \( A(-2,0) \to A'(2,0) \)
       - \( B(0,3) \to B'(0,3) \)
       - \( C(2,2) \to C'(-2,2) \)
  3. **Graph the New Triangle \( A'B'C' \)**: Plot \( A'(2,0) \), \( B'(0,3) \), and \( C'(-2,2) \) and connect them.
  4. **Write the Rule**: The rule for this reflection is \( (x, y) \to (-x, y) \).

---

Would you like a detailed sketch or further explanation? 

### Questions to Expand Learning:
1. What happens if you rotate the triangles 90° counterclockwise instead?
2. How does reflecting over the x-axis change the triangle's coordinates?
3. Can you describe how a 180° rotation differs from a 90° rotation?
4. What would be the result of reflecting over the line \( y = x \)?
5. How can you verify the transformations mathematically without graphing?

**Tip**: Always double-check transformed coordinates by reapplying the transformation rule for accuracy.

Graph the triangle ABC with the given vertices and apply transformations: a 90° clockwise rotation and a reflection over the y-axis.

Understand how to graph a triangle on the Cartesian plane and apply transformations, including a 90° clockwise rotation about the origin and a reflection over the y-axis. This guide provides detailed step-by-step solutions with rules for coordinate changes.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation