Question

A line segment has the endpoints V(1, 75) and W(71, 77). 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 \( V(x_1, y_1) \) and \( W(x_2, y_2) \), we can use the midpoint formula:

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

Given the endpoints \( V(1, 75) \) and \( W(71, 77) \):

- \( x_1 = 1 \)
- \( y_1 = 75 \)
- \( x_2 = 71 \)
- \( y_2 = 77 \)

Now, substitute these values into the midpoint formula:

\[
M = \left( \frac{1 + 71}{2}, \frac{75 + 77}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{1 + 71}{2} = \frac{72}{2} = 36
\]

Calculating the y-coordinate:

\[
\frac{75 + 77}{2} = \frac{152}{2} = 76
\]

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

\[
M(36, 76)
\]