https://file.aiquickdraw.com/mathbot/file/1725415067215q41ke3y0.jpg

The image you uploaded shows a diagram with two points, Point A and Point B, connected by a path consisting of two right-angled segments. The lengths of these segments are given as follows:

- The horizontal segment between Point A and the top right corner has a length of **3.143 units**.
- The vertical segment between Point B and the bottom left corner has a length of **5.344 units**.
- The vertical distance from the top right corner down to Point A is **2.13 units**.

The problem likely involves finding the direct distance between Point A and Point B or another related calculation involving these points.

### Steps to solve:

1. **Horizontal Distance Calculation**:
   The total horizontal distance between Point A and Point B can be calculated as the length of the given horizontal segment.

2. **Vertical Distance Calculation**:
   The total vertical distance between Point A and Point B can be calculated by adding the vertical distances (2.13 units from Point A to the top, and 5.344 units from the top to Point B).

3. **Using the Pythagorean Theorem**:
   The direct distance \(d\) between Points A and B can be found using the Pythagorean theorem:
   \[
   d = \sqrt{(\text{horizontal distance})^2 + (\text{vertical distance})^2}
   \]

### Let's perform the calculation:

1. **Horizontal distance**: \( 3.143 \, \text{units} \)
2. **Vertical distance**: \( 2.13 + 5.344 = 7.474 \, \text{units} \)

Now, calculate the direct distance \(d\):

\[
d = \sqrt{(3.143)^2 + (7.474)^2}
\]

Let me compute this.The direct distance between Point A and Point B is approximately **8.108 units**.

Would you like further details on this calculation, or do you have any other questions? Here are some related questions you might consider:

1. How would the distance change if the horizontal or vertical distances were different?
2. What is the significance of the Pythagorean theorem in real-world applications?
3. How would you calculate the midpoint between Point A and Point B?
4. Can you determine the slope of the line connecting Points A and B?
5. What is the area of the right triangle formed by these points?

**Tip:** When dealing with problems involving distances in a plane, it's often helpful to sketch the scenario and use the Pythagorean theorem for accuracy.

Calculate the direct distance between Point A and Point B using the given horizontal and vertical segments.

Learn how to calculate the direct distance between two points by applying the Pythagorean Theorem. This problem involves a step-by-step solution using horizontal and vertical distances. Suitable for students in Grades 8-10.

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