https://file.aiquickdraw.com/mathbot/file/1725414755813airsehk1.jpg

The image shows a question related to calculating the distance between two points (Point A and Point B) on a coordinate plane. The distances provided in the image are:

- Horizontal distance between Point A and Point B: 3.13 units.
- Vertical distance from Point B to the top (or above Point A): 5.34 units.
- Vertical distance from Point A to the top (or above Point A): 0.79 units.

### Solution:

To find the vertical distance between Point A and Point B, subtract the distance from Point A to the top from the distance from Point B to the top:

\[
\text{Vertical distance} = 5.34 - 0.79 = 4.55 \text{ units}
\]

Now, use the Pythagorean theorem to find the straight-line distance (hypotenuse) between Point A and Point B. The Pythagorean theorem states:

\[
\text{Distance} = \sqrt{(\text{Horizontal distance})^2 + (\text{Vertical distance})^2}
\]

Substituting the given values:

\[
\text{Distance} = \sqrt{(3.13)^2 + (4.55)^2} 
\]

\[
\text{Distance} = \sqrt{9.7969 + 20.7025} 
\]

\[
\text{Distance} = \sqrt{30.4994} 
\]

\[
\text{Distance} \approx 5.52 \text{ units}
\]

### Answer:

The distance between Point A and Point B is approximately 5.52 units.

Would you like more details or have any other questions?

### Relative Questions:
1. How do you apply the Pythagorean theorem in different scenarios?
2. What other methods can be used to calculate the distance between two points?
3. How can the coordinates of Point A and Point B be determined if the plane is defined?
4. What is the significance of understanding horizontal and vertical distances in coordinate geometry?
5. How can this concept be extended to three-dimensional space?

### Tip:
Remember, the Pythagorean theorem is only applicable in right-angled triangles. Always verify the conditions before applying the theorem!

What is the distance between Point A and Point B?

Learn how to calculate the distance between two points, Point A and Point B, on a coordinate plane using the Pythagorean Theorem. This problem involves determining the horizontal and vertical distances and applying the distance formula. Suitable for high school students in Grades 9-12.

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