In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (√50, −6) and (√2, 6)

Verified step by step guidance

1. Identify the formula for the midpoint of a line segment, which is given by $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.
2. Substitute the given endpoints $(x_1,y_1)=(\sqrt{50},-6)$ and $(x_2,y_2)=(\sqrt{2},6)$ into the formula.
3. Calculate the x-coordinate of the midpoint: $\frac{\sqrt{50}+\sqrt{2}}{2}$.
4. Calculate the y-coordinate of the midpoint: $\frac{-6+6}{2}$.
5. Combine the calculated x and y coordinates to express the midpoint as an ordered pair.

Key Concepts

Midpoint Formula

The midpoint of a line segment in a coordinate plane is calculated using the midpoint formula, which is given by M = ((x1 + x2)/2, (y1 + y2)/2). This formula averages the x-coordinates and the y-coordinates of the endpoints to find the point that is exactly halfway between them.

Coordinate System

A coordinate system is a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical). Each point in this system is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding this system is essential for visualizing and solving problems involving points and line segments.

Square Roots

Square roots are a fundamental concept in algebra, representing a value that, when multiplied by itself, gives the original number. For example, √50 and √2 are square roots that can be simplified or approximated to facilitate calculations. Recognizing how to work with square roots is important when dealing with coordinates that involve irrational numbers.