Find the midpoint of each line segment with the given endpoints. (-7/2, 3/2) and (-5/2, -11/2)

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Recall that the midpoint \( M \) of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula: \[ M = \left( \frac{ x_1 + x_2 }{ 2 }, \frac{ y_1 + y_2 }{ 2 } \right) \]

Identify the coordinates of the given endpoints: \( x_1 = -\frac{7}{2}, \quad y_1 = \frac{3}{2} \) \( x_2 = -\frac{5}{2}, \quad y_2 = -\frac{11}{2} \)

Substitute the values of \( x_1 \) and \( x_2 \) into the midpoint formula for the x-coordinate: \[ x_{mid} = \frac{ -\frac{7}{2} + \left(-\frac{5}{2}\right) }{ 2 } \]

Substitute the values of \( y_1 \) and \( y_2 \) into the midpoint formula for the y-coordinate: \[ y_{mid} = \frac{ \frac{3}{2} + \left(-\frac{11}{2}\right) }{ 2 } \]

Simplify both expressions to find the coordinates of the midpoint \( M = (x_{mid}, y_{mid}) \).

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주요 개념

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Midpoint Formula

The midpoint formula calculates the point exactly halfway between two given points in the coordinate plane. It is found by averaging the x-coordinates and the y-coordinates 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.

Fraction Arithmetic

Working with fractions involves operations like addition, subtraction, and division. When finding midpoints with fractional coordinates, it is important to correctly add fractions and divide by 2, often requiring finding common denominators. Accurate fraction manipulation ensures precise midpoint calculation.