In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (-7/2, 3/2) and (-5/2, -11/2)

Verified step by step guidance

Identify the formula for the midpoint of a line segment, which is given by: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).

Substitute the given endpoints \((-\frac{7}{2}, \frac{3}{2})\) and \((-\frac{5}{2}, -\frac{11}{2})\) into the formula, where \(x_1 = -\frac{7}{2}\), \(y_1 = \frac{3}{2}\), \(x_2 = -\frac{5}{2}\), and \(y_2 = -\frac{11}{2}\).

Calculate the x-coordinate of the midpoint: \( \frac{-\frac{7}{2} + (-\frac{5}{2})}{2} \).

Calculate the y-coordinate of the midpoint: \( \frac{\frac{3}{2} + (-\frac{11}{2})}{2} \).

Combine the calculated x and y coordinates to express the midpoint as \( M = \left( \text{calculated x-coordinate}, \text{calculated y-coordinate} \right) \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Midpoint Formula

The midpoint formula is used to find the midpoint of a line segment defined by two endpoints in a coordinate plane. It is given by the formula M = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints. This formula calculates the average of the x-coordinates and the average of the y-coordinates, resulting in the coordinates of the midpoint.

Coordinate Plane

A 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 the plane is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding the coordinate plane is essential for visualizing and solving problems involving points and line segments.

Ordered Pairs

Ordered pairs are pairs of numbers used to represent points in a coordinate system, typically written in the form (x, y). The first number 'x' corresponds to the horizontal position, while the second number 'y' corresponds to the vertical position. Recognizing and manipulating ordered pairs is crucial for performing operations such as finding midpoints, distances, and slopes in algebra.

Watch next

Master Relations and Functions with a bite sized video explanation from Patrick

Start learning