The points ​(StartRoot 3 EndRoot​,negative 3​) and ​(StartRoot 5 EndRoot​,4​) are endpoints of the diameter of a circle. Determine the center of the circle. Find the center of the circle

To find the center of the circle when given the endpoints of the diameter, you can use the midpoint formula. The midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

Given the endpoints \((\sqrt{3}, -3)\) and \((\sqrt{5}, 4)\), the coordinates of the center of the circle (which is the midpoint of the diameter) can be calculated as follows:

\[
\text{Center} = \left(\frac{\sqrt{3} + \sqrt{5}}{2}, \frac{-3 + 4}{2}\right)
\]

Now, compute each coordinate:

1. **For the x-coordinate**:
\[
\frac{\sqrt{3} + \sqrt{5}}{2}
\]

2. **For the y-coordinate**:
\[
\frac{-3 + 4}{2} = \frac{1}{2} = 0.5
\]

So, the center of the circle is:

\[
\left(\frac{\sqrt{3} + \sqrt{5}}{2}, 0.5\right)
\]

This is the center of the circle.

Would you like to go into more details or have any questions?

Here are five related questions:
1. How do you find the radius of the circle given the endpoints of the diameter?
2. What is the equation of the circle with this center and radius?
3. How do you find the area of the circle given the radius?
4. How do you verify if a point lies on the circle given its equation?
5. Can you determine the circumference of the circle using the radius?

**Tip:** Remember that the midpoint formula can also help find the center of a line segment in various coordinate geometry problems.

Learn how to find the center of a circle when given the endpoints of the diameter. This problem involves using the midpoint formula to calculate the coordinates of the circle's center. Suitable for high school students studying coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation