Question

find the midpoint of the segment with the given endpoints.
A(-4, 6) and B (10, -10)

Answer 1

To find the midpoint of the segment with endpoints \( A(-4, 6) \) and \( B(10, -10) \), you can use the midpoint formula:

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

where \( (x_1, y_1) \) are the coordinates of point \( A \) and \( (x_2, y_2) \) are the coordinates of point \( B \).

Given the coordinates:
- \( A(-4, 6) \) means \( x_1 = -4 \) and \( y_1 = 6 \)
- \( B(10, -10) \) means \( x_2 = 10 \) and \( y_2 = -10 \)

Substituting these values into the formula:

\[
M = \left( \frac{-4 + 10}{2}, \frac{6 + (-10)}{2} \right)
\]

Now calculate the x-coordinate:

\[
\frac{-4 + 10}{2} = \frac{6}{2} = 3
\]

Next, calculate the y-coordinate:

\[
\frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

Thus, the midpoint \( M \) is:

\[
M(3, -2)
\]

So, the midpoint of the segment with endpoints \( A(-4, 6) \) and \( B(10, -10) \) is \( \boxed{(3, -2)} \).