Find the midpoint of each line segment with the given endpoints. (-2, -8) and (−6, −2)

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Recall the midpoint formula for a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\): \[\text{Midpoint} = \left( \frac{\,x_1 + x_2}{2}, \frac{\,y_1 + y_2}{2} \right)\]

Identify the coordinates of the given endpoints: \(x_1 = -2, y_1 = -8\) and \(x_2 = -6, y_2 = -2\).

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

Simplify the expressions inside the parentheses by performing the addition in the numerators: \[\left( \frac{-2 - 6}{2}, \frac{-8 - 2}{2} \right)\]

Calculate the final coordinates of the midpoint by dividing each sum by 2: \[\left( \frac{-8}{2}, \frac{-10}{2} \right)\]

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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 identified 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 coordinate geometry.

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.