Find the distance between the points (1,8) and (9,2).

To find the distance between the points \( (1, 8) \) and \( (9, 2) \), we use the **distance formula**:

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

Where \( (x_1, y_1) = (1, 8) \) and \( (x_2, y_2) = (9, 2) \).

Now, substitute the values:

\[
d = \sqrt{(9 - 1)^2 + (2 - 8)^2}
\]

\[
d = \sqrt{(8)^2 + (-6)^2}
\]

\[
d = \sqrt{64 + 36}
\]

\[
d = \sqrt{100}
\]

\[
d = 10
\]

So, the distance between the points is **10 units**.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:
1. How would the formula change if we used three-dimensional points?
2. What is the midpoint between the points (1, 8) and (9, 2)?
3. How can we apply the distance formula in real-life scenarios like map reading?
4. Can you find the equation of the line passing through these two points?
5. What is the slope of the line connecting these points?

**Tip:** The distance formula is derived from the Pythagorean Theorem, so it's essentially finding the hypotenuse of a right triangle formed by the points.

Learn how to calculate the distance between the points (1, 8) and (9, 2) using the distance formula. This step-by-step guide covers key geometry concepts and applies the Pythagorean Theorem. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation