Question

A line segment has the endpoints T(4, 2) and U(0, –8). Find the coordinates of its midpoint M. Write the coordinates as decimals or integers.

Answer 1

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

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

In this case, the coordinates of the endpoints are:
- \( T(4, 2) \) which gives \( x_1 = 4 \) and \( y_1 = 2 \)
- \( U(0, -8) \) which gives \( x_2 = 0 \) and \( y_2 = -8 \)

Now we can substitute these values into the midpoint formula:

\[
M = \left(\frac{4 + 0}{2}, \frac{2 + (-8)}{2}\right)
\]

Calculating the x-coordinate of the midpoint:
\[
\frac{4 + 0}{2} = \frac{4}{2} = 2
\]

Calculating the y-coordinate of the midpoint:
\[
\frac{2 + (-8)}{2} = \frac{2 - 8}{2} = \frac{-6}{2} = -3
\]

Thus, the coordinates of the midpoint \( M \) are:
\[
M(2, -3)
\]

So, the coordinates of the midpoint are \( \boxed{(2, -3)} \).