Find the midpoint of each line segment with the given endpoints. (6, 8) and (2, 4)

Verified step by step guidance

1. Recall the midpoint formula for a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\): \[\text{Midpoint} = \left( \frac{\,x_1 + x_2}{2}, \frac{\,y_1 + y_2}{2} \right)\]
2. Identify the coordinates of the given endpoints: \( (x_1, y_1) = (6, 8) \) and \( (x_2, y_2) = (2, 4) \).
3. Substitute the values of \(x_1\), \(x_2\), \(y_1\), and \(y_2\) into the midpoint formula: \[\left( \frac{6 + 2}{2}, \frac{8 + 4}{2} \right)\]
4. Simplify the expressions inside the parentheses by adding the coordinates: \[\left( \frac{8}{2}, \frac{12}{2} \right)\]
5. Finally, divide each sum by 2 to find the midpoint coordinates: \[\left( 4, 6 \right)\]

Key Concepts

Midpoint Formula

The midpoint formula calculates the point exactly halfway between two given points in a coordinate plane. It is found by averaging the x-coordinates and the y-coordinates of the endpoints separately: Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2). This formula helps locate the center of a line segment.

Coordinate Plane

The coordinate plane is a two-dimensional surface defined by a horizontal x-axis and a vertical y-axis. Points are represented as ordered pairs (x, y), where x indicates horizontal position and y indicates vertical position. Understanding this system is essential for plotting points and calculating distances or midpoints.

Line Segment

A line segment is a part of a line bounded by two distinct endpoints. Unlike a line, it has a fixed length. Knowing the endpoints of a line segment allows for calculations such as length, midpoint, and slope, which are fundamental in coordinate geometry.