uction to Question 17, 1.1.55 HW Score: $$ 36.67 \% $$, 11 of 30 points Points: 0 of 1 Save The points $$ (-7,-4) $$ and $$ (3,5) $$ are the endpoints of the diameter of a circle. Find the length of the radius of the circle

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To find the length of the radius of the circle when given the endpoints of its diameter, follow these steps:

1. **Identify the Endpoints:**
   - Point $$ A(-7, -4) $$
   - Point $$ B(3, 5) $$

2. **Calculate the Distance Between Points $$ A $$ and $$ B $$:**
   
   The distance between two points in a plane is given by the distance formula:
   $$
   \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   $$
   
   Plugging in the coordinates:
   $$
   \text{Distance} = \sqrt{(3 - (-7))^2 + (5 - (-4))^2}
   $$
   $$
   \text{Distance} = \sqrt{(10)^2 + (9)^2}
   $$
   $$
   \text{Distance} = \sqrt{100 + 81}
   $$
   $$
   \text{Distance} = \sqrt{181}
   $$
   
   So, the **diameter** of the circle is $$ \sqrt{181} $$ units.

3. **Find the Radius:**

The radius $$ r $$ is half of the diameter $$ d $$:
   $$
   r = \frac{d}{2} = \frac{\sqrt{181}}{2}
   $$
   
   **Approximate Value:**
   
   If you need a decimal approximation:
   $$
   \sqrt{181} \approx 13.45
   $$
   $$
   r \approx \frac{13.45}{2} \approx 6.725
   $$
   
   So, the **radius** of the circle is approximately **6.725 units**.

**Final Answer:**  
The radius of the circle is $$ \frac{\sqrt{181}}{2} $$ units, which is approximately 6.725 units.
The radius of the circle is $$ \frac{\sqrt{181}}{2} $$ units, approximately 6.725 units.

uction to Question 17, 1.1.55 HW Score: \( 36.67 \% \), 11 of 30 points Points: 0 of 1 Save The points \( (-7,-4) \) and \( (3,5) \) are the endpoints of the diameter of a circle. Find the length of the radius of the circle

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