https://file.aiquickdraw.com/mathbot/file/1724425990132dsc8n4g1.jpg

Find the distance between the points. Round to two decimal places if necessary.

To find the distance between the two points on the graph, we can use the distance formula:

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

### Step 1: Identify the coordinates of the points
From the graph:
- The first point (A) is at \((4, 1)\).
- The second point (B) is at \((8, -2)\).

### Step 2: Plug the coordinates into the distance formula
\[
d = \sqrt{(8 - 4)^2 + (-2 - 1)^2}
\]

### Step 3: Calculate the differences and squares
\[
d = \sqrt{(4)^2 + (-3)^2}
\]
\[
d = \sqrt{16 + 9}
\]

### Step 4: Add the squares
\[
d = \sqrt{25}
\]

### Step 5: Take the square root
\[
d = 5
\]

So, the distance between the two points is \(5\) units.

Would you like any more details or explanations?

---

Here are five questions you might find interesting:

1. How would the distance formula change if the coordinates included fractions or decimals?
2. Can you use the distance formula to find the distance between any two points in 3D space?
3. How can you verify that the points used are plotted correctly on the graph?
4. What is the relationship between the distance formula and the Pythagorean theorem?
5. How would you calculate the midpoint between these two points?

**Tip:** Always check the coordinates carefully when using the distance formula to avoid calculation errors.

Learn how to find the distance between two points on a graph using the distance formula. This problem involves calculating the distance between points (4, 1) and (8, -2) with a detailed step-by-step solution. Suitable for 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