https://file.aiquickdraw.com/mathbot/file/1727110371869366qx21r.jpg

To solve this, we need to calculate the circumference and area of the circle based on the given diagram, where each unit on the graph is 1 centimeter.

### Step 1: Identify the radius of the circle
The center of the circle is at point \( X(-3, 4) \), and the point on the edge of the circle is at \( Y(-4, 2) \). The distance between these two points represents the radius of the circle. To find this distance, we use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Where \( (x_1, y_1) = (-3, 4) \) and \( (x_2, y_2) = (-4, 2) \):

\[
d = \sqrt{((-4 - (-3))^2 + (2 - 4)^2)} = \sqrt{((-4 + 3)^2 + (2 - 4)^2)} = \sqrt{((-1)^2 + (-2)^2)} = \sqrt{(1 + 4)} = \sqrt{5} \approx 2.24 \, \text{cm}
\]

Thus, the radius \( r \) is approximately \( 2.24 \, \text{cm} \).

### Step 2: Calculate the circumference
The formula for the circumference of a circle is:

\[
C = 2\pi r
\]

Substituting \( r = 2.24 \, \text{cm} \):

\[
C = 2 \pi (2.24) \approx 14.1 \, \text{cm}
\]

### Step 3: Calculate the area
The formula for the area of a circle is:

\[
A = \pi r^2
\]

Substituting \( r = 2.24 \, \text{cm} \):

\[
A = \pi (2.24)^2 \approx \pi (5.02) \approx 15.8 \, \text{cm}^2
\]

### Final Answers:
- **Circumference**: \( 14.1 \, \text{cm} \)
- **Area**: \( 15.8 \, \text{cm}^2 \)

Would you like more details or have any further questions?

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Here are five related questions:
1. How would the circumference change if the radius doubled?
2. What formula would you use to calculate the area of a sector of the circle?
3. If each unit on the graph represented 2 cm, how would the circumference and area change?
4. How does the distance formula relate to the Pythagorean theorem?
5. Can you generalize the method to find the area and circumference for any circle given its center and a point on its edge?

**Tip**: Always double-check the units in problems involving geometry, as even small changes can significantly affect the outcome.

Find the circumference and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.

Learn how to calculate the circumference and area of a circle using graph coordinates with the center at (-3, 4) and a point on the edge at (-4, 2). This problem involves applying the distance formula, circumference, and area formulas to find the radius, circumference, and area of the circle.

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