Determine the midpoint of a line segment

The midpoint of a line segment in the coordinate plane is the point exactly halfway between its endpoints, having equal distances to both endpoints. Its coordinates are found by averaging the corresponding coordinates separately, $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ , including when coordinates are negative, fractional, or decimal; this is distinct from averaging the endpoints’ distances or combining coordinates across axes.

Detailed Explanation: Determine the midpoint of a line segment

The midpoint is the point exactly halfway between the two endpoints of a line segment. To find it, average the $x$ -coordinates and average the $y$ -coordinates separately:

\text{Midpoint}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)

Example

Find the midpoint of the segment with endpoints $A(-3,4)$ and $B(5,-2)$ .

1. Average the $x$ -coordinates.

\frac{-3+5}{2}=\frac{2}{2}=1

2. Average the $y$ -coordinates.

\frac{4+(-2)}{2}=\frac{2}{2}=1

3. Combine the results in order.

\boxed{(1,1)}

So, the midpoint of $\overline{AB}$ is $(1,1)$ . Remember to average corresponding coordinates: $x$ with $x$ and $y$ with $y.

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Line Segment (Points) - Find Midpoint (Coordinate)

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