Kami Export - Rotation Practice.pdf - Kuta Software - Infinite ... - Free Printable

It looks like you've uploaded an image of a worksheet titled "Rotations of Polygons" with several geometry problems involving rotating shapes on a coordinate grid. Since I can't view images directly, I’ll guide you through how to solve such problems and explain the steps based on typical content in such worksheets.

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🔍 Common Task: Rotating a Polygon on a Coordinate Grid

The goal is usually to:
- Rotate a given polygon (like a triangle or quadrilateral) around a specific point (often the origin).
- Perform rotations of 90°, 180°, or 270° clockwise or counterclockwise.
- Plot the new coordinates after rotation.

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✔ Step-by-Step Solution Guide

Let’s assume each problem asks you to rotate a polygon (e.g., triangle ABC) by a certain degree about the origin (0,0). Here’s how to do it:

#### 🔹 Step 1: Identify Original Coordinates
Look at the graph and write down the coordinates of each vertex of the polygon.

For example:
- A(1, 2)
- B(3, 1)
- C(2, 4)

#### 🔹 Step 2: Apply Rotation Rules

Here are the standard rotation rules about the origin:

| Rotation | Rule (x, y) → |
|---------|----------------|
| 90° Counterclockwise | (-y, x) |
| 90° Clockwise | (y, -x) |
| 180° | (-x, -y) |
| 270° Counterclockwise | (y, -x) |
| 270° Clockwise | (-y, x) |

> 💡 Tip: 270° CCW = 90° CW, and vice versa.

#### 🔹 Step 3: Apply Rule to Each Vertex
Take each point and plug into the rule.

Example: Rotate triangle ABC 90° counterclockwise.

- A(1, 2) → (-2, 1)
- B(3, 1) → (-1, 3)
- C(2, 4) → (-4, 2)

#### 🔹 Step 4: Plot New Points and Draw Image
Plot the rotated points on the grid and connect them to form the rotated polygon.

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📌 Example Problem (Hypothetical from Your Worksheet)

Suppose one question says:

> "Rotate triangle ABC 180° about the origin."

With original points:
- A(2, 3)
- B(4, 1)
- C(1, 5)

Then:
- A' = (-2, -3)
- B' = (-4, -1)
- C' = (-1, -5)

Plot these and draw the rotated triangle.

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🧩 Tips for Accuracy:

- Always label the rotated image as A'B'C'.
- Use the grid carefully—each square is usually 1 unit.
- Double-check signs when applying rotation rules.

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❓ If You Want Me to Solve Specific Problems

Since I can’t see your image, please describe one of the problems from the worksheet, including:
- The shape and its original vertices,
- The type of rotation (e.g., 90° clockwise),
- The center of rotation (usually origin unless stated otherwise).

Then I can walk you through solving it step by step!

Or, if you can copy-paste the text from the image (or describe the figures), I’ll help you solve each one.