In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)

Verified step by step guidance

1. Identify the formula for the midpoint of a line segment, which is given by \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).
2. Substitute the given endpoints \((-3, -4)\) and \((6, -8)\) into the formula, where \(x_1 = -3\), \(y_1 = -4\), \(x_2 = 6\), and \(y_2 = -8\).
3. Calculate the x-coordinate of the midpoint: \( \frac{-3 + 6}{2} \).
4. Calculate the y-coordinate of the midpoint: \( \frac{-4 + (-8)}{2} \).
5. Combine the calculated x and y coordinates to express the midpoint as \( M = \left( \frac{-3 + 6}{2}, \frac{-4 + (-8)}{2} \right) \).

Key Concepts

Midpoint Formula

The midpoint formula is used to find the point that is exactly halfway between two given points in a coordinate plane. It is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints. This concept is essential for determining the midpoint of a line segment.

Coordinate Plane

The coordinate plane is a two-dimensional surface formed by the intersection of a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is represented by an ordered pair (x, y), which indicates its position relative to the axes. Understanding the coordinate plane is crucial for visualizing and solving problems involving points and line segments.

Ordered Pairs

Ordered pairs are pairs of numbers used to represent the coordinates of a point in the coordinate plane. The first number corresponds to the x-coordinate, and the second number corresponds to the y-coordinate. Recognizing and manipulating ordered pairs is fundamental for applying the midpoint formula and performing other geometric calculations.