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To determine the length of interval \( AC \) on the graph, we need to find the coordinates of points \( A \) and \( C \), and then use the distance formula.

1. **Identifying Coordinates**: 
   - Point \( A \) appears to be at coordinates \((-4, 10)\).
   - Point \( C \) appears to be at coordinates \((10, 2)\).

2. **Applying the Distance Formula**:
   The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   Substituting the coordinates of points \( A \) and \( C \):
   \[
   d = \sqrt{(10 - (-4))^2 + (2 - 10)^2}
   \]
   \[
   d = \sqrt{(14)^2 + (-8)^2}
   \]
   \[
   d = \sqrt{196 + 64}
   \]
   \[
   d = \sqrt{260}
   \]

   Now, calculating the square root of 260 gives us the length of \( AC \). Let's compute this.The length of interval \( AC \) is approximately \( 16.12 \) units when rounded to two decimal places.

Would you like further details on this calculation or have any other questions? Here are some related topics you might find interesting:

1. How to find the midpoint of a line segment on a graph.
2. Deriving the formula for the distance between two points in 3-dimensional space.
3. Understanding Pythagoras' theorem and its applications in coordinate geometry.
4. Calculating the slope of a line segment between two points.
5. Exploring different methods to calculate distances in non-Euclidean geometries.

**Tip:** Always check the coordinates and calculations twice when solving geometry problems to ensure accuracy.

Consider the interval AC that has been graphed on the number plane. Find the length of interval AC, rounding your answer to two decimal places.

This problem involves finding the length of interval AC on a coordinate plane using the distance formula. By identifying the coordinates of points A and C, the solution is calculated as approximately 16.12 units. This solution is ideal for students in Grades 8-10 studying coordinate geometry.

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