Question

A line segment has the endpoints U(8, 4) and V(10, 8). Find the coordinates of its midpoint M. Write the coordinates as decimals or integers.

Answer 1

To find the midpoint \( M \) of a line segment with endpoints \( U(x_1, y_1) \) and \( V(x_2, y_2) \), we use the midpoint formula:

\[
M\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

For the endpoints \( U(8, 4) \) and \( V(10, 8) \):

- \( x_1 = 8 \), \( y_1 = 4 \)
- \( x_2 = 10 \), \( y_2 = 8 \)

Substituting these values into the formula:

\[
M\left( \frac{8 + 10}{2}, \frac{4 + 8}{2} \right)
\]

Calculating each coordinate:

1. For the \( x \)-coordinate:
\[
\frac{8 + 10}{2} = \frac{18}{2} = 9
\]

2. For the \( y \)-coordinate:
\[
\frac{4 + 8}{2} = \frac{12}{2} = 6
\]

Therefore, the coordinates of the midpoint \( M \) are:

\[
M(9, 6)
\]