Question

A line segment has the endpoints G(4,2) and H(-6,-6) 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 \( G(4, 2) \) and \( H(-6, -6) \), we can use the midpoint formula:

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

Where \( (x_1, y_1) \) are the coordinates of point \( G \) and \( (x_2, y_2) \) are the coordinates of point \( H \).

Substituting in the coordinates:

- \( x_1 = 4 \)
- \( y_1 = 2 \)
- \( x_2 = -6 \)
- \( y_2 = -6 \)

Now plug these values into the formula:

\[
M = \left( \frac{4 + (-6)}{2}, \frac{2 + (-6)}{2} \right)
\]

Calculating the x-coordinate:

\[
\frac{4 - 6}{2} = \frac{-2}{2} = -1
\]

Calculating the y-coordinate:

\[
\frac{2 - 6}{2} = \frac{-4}{2} = -2
\]

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

\[
M = (-1, -2)
\]

So, the final answer is:

\[
M = (-1, -2)
\]