Find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)

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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: \( (x_1, y_1) = (-3, -4) \) and \( (x_2, y_2) = (6, -8) \).

Substitute the values into the midpoint formula: \[ M = \left( \frac{ -3 + 6 }{ 2 }, \frac{ -4 + (-8) }{ 2 } \right) \]

Simplify the expressions inside the parentheses separately: \[ \frac{ -3 + 6 }{ 2 } = \frac{3}{2} \quad \text{and} \quad \frac{ -4 + (-8) }{ 2 } = \frac{ -12 }{ 2 } \]

Write the midpoint as the ordered pair using the simplified values: \[ M = \left( \frac{3}{2}, -6 \right) \]

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주요 개념

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Coordinate Plane and Points

The coordinate plane is a two-dimensional system where each point is defined by an ordered pair (x, y). Understanding how to plot and interpret points is essential for visualizing line segments and their properties.

Line Segment

A line segment is the part of a line bounded by two endpoints. Knowing the endpoints allows us to analyze properties like length and midpoint, which are fundamental in geometry and algebra.

Midpoint Formula

The midpoint formula calculates the point exactly halfway between two endpoints. It is given by ((x1 + x2)/2, (y1 + y2)/2), averaging the x-coordinates and y-coordinates separately to find the midpoint.