what is the midpoint of the line segment graphed below

2 min read 21-12-2024

what is the midpoint of the line segment graphed below

Finding the Midpoint: A Step-by-Step Guide

Title Tag: Find the Midpoint: Easy Steps & Examples

Meta Description: Learn how to easily calculate the midpoint of a line segment using a simple formula. This guide provides a step-by-step explanation with clear examples and visuals. Perfect for students and anyone needing a refresher on coordinate geometry!

(Note: To complete this article, I need the graph. Please provide the coordinates of the endpoints of the line segment.)

Let's assume the line segment has endpoints A and B, with coordinates A(x₁, y₁) and B(x₂, y₂). Once you provide the coordinates, I can substitute them into the formula and show you the calculation.

Understanding the Midpoint Formula

The midpoint of a line segment is the point that divides the segment into two equal parts. It's the exact middle! We can find its coordinates using a simple formula:

Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

This formula calculates the average of the x-coordinates and the average of the y-coordinates to find the midpoint's coordinates.

Step-by-Step Calculation

1. Identify the Coordinates: First, clearly identify the x and y coordinates of each endpoint (A and B) from the provided graph. Let's say (for example) A = (2, 4) and B = (8, 10).

2. Apply the Midpoint Formula: Substitute the coordinates into the midpoint formula:

M = ((2 + 8) / 2, (4 + 10) / 2)

3. Simplify the Expression: Perform the addition and division:

M = (10 / 2, 14 / 2)

M = (5, 7)

4. State the Midpoint: The midpoint of the line segment with endpoints A(2, 4) and B(8, 10) is (5, 7).

Visual Representation

(Insert a graph here showing the line segment with endpoints A and B, and the midpoint M clearly marked.)

This visual representation will help solidify your understanding. You can see that the point (5, 7) perfectly bisects the line segment AB.

Practice Problems (Optional)

To further solidify your understanding, try these practice problems:

Problem 1: Find the midpoint of a line segment with endpoints C(-3, 2) and D(5, -4).
Problem 2: If the midpoint of a line segment is (1, -2) and one endpoint is (4, 6), find the coordinates of the other endpoint.

(Provide solutions to the practice problems below the problems themselves)

Conclusion

Finding the midpoint of a line segment is a straightforward process using the midpoint formula. By understanding this formula and practicing with examples, you'll quickly master this essential concept in coordinate geometry. Remember to always carefully identify the coordinates of your endpoints before applying the formula. Provide the graph's coordinates, and I will complete the example for you.