https://file.aiquickdraw.com/mathbot/file/1729457830415a4v9qp0g.jpg

Instructions: Using the image, find the distance between the points given on the graph.

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Distance =√
 Answer 1 Question 23


To find the distance between the two points given in the image, we will use the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

The two points are marked on the graph:
- The first point is \((-5, 4)\)
- The second point is \((4, -5)\)

Now, applying the coordinates to the distance formula:

\[
\text{Distance} = \sqrt{(4 - (-5))^2 + (-5 - 4)^2}
\]

Simplifying:

\[
\text{Distance} = \sqrt{(4 + 5)^2 + (-5 - 4)^2}
\]

\[
\text{Distance} = \sqrt{9^2 + (-9)^2}
\]

\[
\text{Distance} = \sqrt{81 + 81}
\]

\[
\text{Distance} = \sqrt{162}
\]

\[
\text{Distance} = \sqrt{81 \times 2} = 9\sqrt{2}
\]

Thus, the distance between the two points is:

\[
\boxed{9\sqrt{2}}
\]

Would you like further details on how this formula is applied or any other clarification?

### Related Questions:
1. How do you derive the distance formula from the Pythagorean theorem?
2. How can the slope of this line be calculated using the two points?
3. What is the midpoint of the two points on the graph?
4. How would you find the equation of the line passing through these points?
5. How does the distance between points change if we scale the graph?

### Tip:
The distance formula is directly related to the Pythagorean theorem, which connects the horizontal and vertical differences (legs of a right triangle) between two points to their direct distance (the hypotenuse).

Using the image, find the distance between the points given on the graph.

Learn how to calculate the distance between the two points (-5, 4) and (4, -5) on a graph using the distance formula √((x2 - x1)^2 + (y2 - y1)^2). This solution is suitable for students in Grades 8-10 and is based on key concepts from analytic geometry and the Pythagorean Theorem.

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