Line segment XY has endpoints at X(-6,4) and Y(4,6). What are the coordinates of the midpoint of the line segment?

The formula for the midpoint of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

For the endpoints \(X(-6, 4)\) and \(Y(4, 6)\), substitute the values into the formula:

\[
\left( \frac{-6 + 4}{2}, \frac{4 + 6}{2} \right)
= \left( \frac{-2}{2}, \frac{10}{2} \right)
= (-1, 5)
\]

Thus, the coordinates of the midpoint are \((-1, 5)\).

Would you like further clarification or details on how the formula works?

Here are 5 related questions for further practice:
1. What is the length of the line segment with endpoints at \( (-6,4) \) and \( (4,6) \)?
2. How do you calculate the slope of the line passing through \( X(-6, 4) \) and \( Y(4, 6) \)?
3. If the midpoint is \((-1, 5)\), what would be the equation of the line passing through \( X \) and \( Y \)?
4. Can the midpoint formula be used for three-dimensional points? If so, how?
5. What is the distance from the midpoint \((-1, 5)\) to the point \( X(-6, 4) \)?

**Tip:** The midpoint formula averages the x-coordinates and y-coordinates of the two endpoints, making it a useful tool in geometry for finding a point that divides a segment into two equal parts.

Discover how to find the midpoint of a line segment with endpoints X(-6,4) and Y(4,6) using the midpoint formula. This problem is a great introduction to coordinate geometry for students in Grades 6-8, involving simple calculations to determine the point that divides a line into two equal parts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation