Question

A line segment has the endpoints C(12,-3) and D(16,-7) find the coordinates of its midpoint M
Write the coordinates as decimals or integers
M=

Answer 1

To find the midpoint \( M \) of a line segment with endpoints \( C(x_1, y_1) \) and \( D(x_2, y_2) \), you can use the midpoint formula:

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

For the points \( C(12, -3) \) and \( D(16, -7) \):
- \( x_1 = 12 \)
- \( y_1 = -3 \)
- \( x_2 = 16 \)
- \( y_2 = -7 \)

Now substitute these values into the midpoint formula:

\[
M = \left( \frac{12 + 16}{2}, \frac{-3 + (-7)}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{12 + 16}{2} = \frac{28}{2} = 14
\]

Now calculating the y-coordinate:

\[
\frac{-3 + (-7)}{2} = \frac{-10}{2} = -5
\]

So the coordinates of the midpoint \( M \) are

\[
M = (14, -5)
\]

Thus, \( M = 14, -5 \).