To determine specific points on the graph of the circle, we start with the center and use the radius to find key points along the circle.

### Given:
- **Center**: \((-1, -5)\)
- **Radius**: \(2\)

### Key Points on the Circle:
For a circle centered at \((-1, -5)\) with a radius of \(2\), you can find the following points:

1. **To the right of the center**: 
   \[
   (-1 + 2, -5) = (1, -5)
   \]

2. **To the left of the center**:
   \[
   (-1 - 2, -5) = (-3, -5)
   \]

3. **Above the center**:
   \[
   (-1, -5 + 2) = (-1, -3)
   \]

4. **Below the center**:
   \[
   (-1, -5 - 2) = (-1, -7)
   \]

### List of Points:
- Right: \((1, -5)\)
- Left: \((-3, -5)\)
- Above: \((-1, -3)\)
- Below: \((-1, -7)\)

These four points, along with the center, are significant points on the graph of the circle. Plotting these on a coordinate plane and connecting them smoothly will give you the full circle.

Would you like to dive deeper into how these points are calculated or discuss more about graphing circles?

Here are some related questions:
1. How do you find additional points on a circle other than the key points?
2. How does changing the radius affect the key points on the graph?
3. What is the general method for graphing circles by hand?
4. How do you verify if a point lies on a circle?
5. What is the significance of these key points when analyzing the properties of a circle?

**Tip:** When graphing a circle, always start by plotting the center and then mark points at the distance of the radius directly in the cardinal directions (up, down, left, right) from the center.

Explore how to find key points on the graph of a circle, including the center, points to the right, left, above, and below. This problem covers basic geometry concepts related to circles, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation