https://file.aiquickdraw.com/mathbot/file/1725504435521sz0oxd47.jpg

The problem in the image asks to find the distance between two points, \( (2, 6) \) and \( (7, -6) \), in simplest radical form. To solve this, we can use the distance formula:

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

### Given:
- \( (x_1, y_1) = (2, 6) \)
- \( (x_2, y_2) = (7, -6) \)

### Solution:
1. Subtract the x-coordinates:
   \[
   x_2 - x_1 = 7 - 2 = 5
   \]
2. Subtract the y-coordinates:
   \[
   y_2 - y_1 = -6 - 6 = -12
   \]
3. Plug these into the distance formula:
   \[
   d = \sqrt{(5)^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13
   \]

So, the distance between the two points is \( \boxed{13} \).

Would you like more details or have any questions? Here are some related questions:

1. How do you find the midpoint between two points?
2. What is the formula for the slope between two points?
3. Can you explain how the distance formula is derived from the Pythagorean Theorem?
4. How do you solve for the distance if the points are in 3D space?
5. What are real-world applications of the distance formula?

**Tip**: When solving distance problems, always double-check your subtraction and square values to avoid errors.

Find the distance between the two points (2, 6) and (7, -6) in simplest radical form.

Learn how to find the distance between two points (2, 6) and (7, -6) using the distance formula. This step-by-step solution simplifies the distance to 13, demonstrating key concepts in coordinate geometry. Suitable for students in 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