Find the midpoint of the segment with the following endpoints.

left parenthesis, minus, 2, comma, 3, right parenthesis, and , left parenthesis, minus, 6, comma, 9, right parenthesis

(−2,3) and (−6,9)

To find the midpoint of a line segment given two endpoints, we use the midpoint formula:

\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Given endpoints are \((-2, 3)\) and \((-6, 9)\), where:
- \(x_1 = -2\), \(y_1 = 3\)
- \(x_2 = -6\), \(y_2 = 9\)

Now, apply the midpoint formula:

\[
\text{Midpoint} = \left( \frac{-2 + (-6)}{2}, \frac{3 + 9}{2} \right)
\]

Simplify each coordinate:

\[
\text{Midpoint} = \left( \frac{-8}{2}, \frac{12}{2} \right) = (-4, 6)
\]

Thus, the midpoint of the segment is \((-4, 6)\).

Would you like further details or have any questions?

Here are some related questions you might consider:
1. How do you calculate the distance between two points?
2. How do you find the slope of a line segment between two points?
3. What is the equation of a line given two points?
4. How do you find the equation of the perpendicular bisector of a line segment?
5. How do you use the midpoint formula in three dimensions?

**Tip:** The midpoint formula is useful for dividing a line segment exactly in half!

Find the midpoint of the segment with the following endpoints: (−2,3) and (−6,9)

Learn how to find the midpoint of a line segment with endpoints (−2, 3) and (−6, 9) using the midpoint formula. This problem covers key concepts in coordinate geometry and is suitable 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