https://file.aiquickdraw.com/mathbot/file/172891183713168xz4r3a.pdf

Let's begin by analyzing the questions in your document.

### For the first part:

1. **Figure B is a dilation of figure A. What is the scale factor?**
   - The side length of Figure A is 3, and the side length of Figure B is 9. 
   - The scale factor for dilation is calculated by dividing the side length of Figure B by the side length of Figure A:  
     \[
     \text{Scale factor} = \frac{\text{Side length of B}}{\text{Side length of A}} = \frac{9}{3} = 3.
     \]
     Therefore, the correct answer is **3**.

### For the second part (Grid Slope):

2. **Each square on a grid represents 1 unit on each side. Calculate the slope of the graph.**
   - To calculate the slope of a graph, you can use the formula:
     \[
     \text{Slope} = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}.
     \]
   - From the image, identify two points on the line and calculate the rise (the change in \(y\)-coordinates) and the run (the change in \(x\)-coordinates).
     For example, if two points on the graph are \((0, 0)\) and \((3, 2)\), then:
     \[
     \text{Slope} = \frac{2 - 0}{3 - 0} = \frac{2}{3}.
     \]

### For the history questions:

3. **When was Jamestown, the first permanent English settlement in America, founded?**
   - Jamestown was founded in **1607** (option A).

4. **Which colony was originally settled by the Dutch in an area known for its deep harbors and access to the sea?**
   - The colony originally settled by the Dutch was **New York** (option D).

5. **Which colony, known for its commitment to religious freedom, was founded by Roger Williams after he was expelled from Massachusetts?**
   - **Rhode Island** (option C) was founded by Roger Williams.

6. **Which colony was established by Pilgrims seeking religious freedom?**
   - **Plymouth Colony, Massachusetts** (option A) was established by Pilgrims.

### For the open-ended questions:

7. **Why did James Oglethorpe found the colony of Georgia?**
   - Two correct answers:
     - **To create a buffer between the English Colonies and Spanish Florida.**
     - **To create a haven for people who owed money.**
   
8. **Prompt: How geographical features influenced the development of the 13 colonies.**
   - The geographical features, such as the fertile soil in the Southern Colonies, allowed for the establishment of large plantations, influencing the economy towards agriculture, particularly tobacco, rice, and indigo. In contrast, the Northern Colonies had a rockier terrain, leading them to focus more on shipbuilding, trade, and fishing. The middle colonies, with their moderate climate and good harbors, developed a mix of agriculture and commerce.

Would you like further details on any of these responses?

### Here are 5 relative questions for further learning:

1. What is the process to verify the accuracy of a dilation transformation?
2. How do you determine the equation of a line given two points?
3. How did the triangular trade influence the economic development of the 13 colonies?
4. What role did religion play in the establishment of other colonies besides Rhode Island?
5. What was the impact of the geographical divide between Northern and Southern colonies on their respective social structures?

### Tip:
In graphing, always check two clear points on the line to ensure the most accurate slope calculation.

Find the slope of the line that passes through (10, -8) and (1, 12).

Learn how to calculate the slope of a line passing through the points (10, -8) and (1, 12) using the slope formula. This guide covers key concepts in coordinate geometry and provides a step-by-step solution. Suitable for Grades 6-9.

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