https://file.aiquickdraw.com/mathbot/file/17272140708313qqse9ou.jpg

To solve this problem, we need to determine the radius of the circle, which we can obtain by finding the distance between points \( X(-3, 4) \) (the center) and \( Y(-4, 2) \) (a point on the circumference). The formula for the distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

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

### Step 1: Find the radius
Here, the center is \( (-3, 4) \) and the point on the circumference is \( (-4, 2) \).

\[
d = \sqrt{((-4) - (-3))^2 + (2 - 4)^2}
\]
\[
d = \sqrt{(-4 + 3)^2 + (2 - 4)^2}
\]
\[
d = \sqrt{(-1)^2 + (-2)^2}
\]
\[
d = \sqrt{1 + 4} = \sqrt{5} \approx 2.2 \, \text{cm}
\]

So, the radius \( r \approx 2.2 \, \text{cm} \).

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

\[
C = 2 \pi r
\]

Substitute \( r = 2.2 \):

\[
C = 2 \pi \times 2.2 \approx 13.8 \, \text{cm}
\]

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

\[
A = \pi r^2
\]

Substitute \( r = 2.2 \):

\[
A = \pi \times (2.2)^2 = \pi \times 4.84 \approx 15.2 \, \text{cm}^2
\]

### Final Answers:
- **Circumference**: \( 13.8 \, \text{cm} \)
- **Area**: \( 15.2 \, \text{cm}^2 \)

Would you like further details or have any questions?

Here are some related questions:
1. How would the circumference change if the radius doubled?
2. What is the diameter of the circle?
3. How can the distance formula be generalized for 3D space?
4. What is the relationship between circumference and area for a circle?
5. How would the area change if the radius was halved?

**Tip**: When working with circles, remember that both the area and circumference scale differently as the radius changes.

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 find the circumference and area of a circle from a graph with given points. Use the distance formula, along with circle geometry formulas, to calculate the circumference and area. The solution provides a detailed step-by-step explanation suitable for students in Grades 7-9.

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