Question

A line segment has the endpoints V(9, 61) and W(75, 85). 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 use the midpoint formula:

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

For the given points \( V(9, 61) \) and \( W(75, 85) \):

- \( x_1 = 9 \)
- \( y_1 = 61 \)
- \( x_2 = 75 \)
- \( y_2 = 85 \)

Now, we can calculate the coordinates of the midpoint \( M \):

1. Calculate the x-coordinate of \( M \):
\[
M_x = \frac{9 + 75}{2} = \frac{84}{2} = 42
\]

2. Calculate the y-coordinate of \( M \):
\[
M_y = \frac{61 + 85}{2} = \frac{146}{2} = 73
\]

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

\[
M(42, 73)
\]