Midpoint of a Line Segment: Your Complete Guide with Worked Examples

📚 Quick Study Guide

• 📍 Definition: The midpoint is the point exactly halfway between two endpoints of a line segment.
• 📐 Formula: Given two points $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint $M$ is calculated as: $M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$.
• ➕ How to use it: Simply add the x-coordinates of the endpoints, divide by 2, and do the same for the y-coordinates.
• 🧭 Important Note: The midpoint is always a point, so it's represented as an ordered pair (x, y).

✏️ Practice Quiz

1. What is the midpoint of the line segment with endpoints (2, 4) and (6, 8)?
   1. (4, 6)
   2. (8, 12)
   3. (2, 2)
   4. (4, 12)
2. Find the midpoint of the line segment with endpoints (-1, 5) and (3, -1).
   1. (2, 4)
   2. (1, 2)
   3. (4, 4)
   4. (-2, 6)
3. If the midpoint of a line segment is (0, 0) and one endpoint is (4, -2), what is the other endpoint?
   1. (-4, 2)
   2. (4, 2)
   3. (-2, 1)
   4. (2, -1)
4. What is the midpoint of the line segment connecting (a, b) and (c, d)?
   1. $(\frac{a+c}{2}, \frac{b+d}{2})$
   2. $(\frac{a-c}{2}, \frac{b-d}{2})$
   3. $(a+c, b+d)$
   4. $(a-c, b-d)$
5. Calculate the midpoint of the line segment with endpoints (-5, -3) and (7, 1).
   1. (1, -1)
   2. (2, -2)
   3. (6, 4)
   4. (-6, -4)
6. The endpoints of a line segment are (0, 6) and (0, -2). What is the midpoint?
   1. (0, 2)
   2. (0, 4)
   3. (0, -4)
   4. (0, -2)
7. Find the midpoint of the line segment with endpoints (2.5, 3.5) and (4.5, 1.5).
   1. (3.5, 2.5)
   2. (7, 5)
   3. (1, 1)
   4. (2, 2)