Question

Calculate the midpoint M of segment AB.
A: (-1,2) B: (4,-2)

Answer 1

To find the midpoint \( M \) of a line segment connecting two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), we use the midpoint formula:

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

Given the points:

- \( A(-1, 2) \) where \( x_1 = -1 \) and \( y_1 = 2 \)
- \( B(4, -2) \) where \( x_2 = 4 \) and \( y_2 = -2 \)

Now, substituting the coordinates into the midpoint formula:

\[
M = \left( \frac{-1 + 4}{2}, \frac{2 + (-2)}{2} \right)
\]

Calculating the \( x \)-coordinate:

\[
\frac{-1 + 4}{2} = \frac{3}{2} = 1.5
\]

Calculating the \( y \)-coordinate:

\[
\frac{2 - 2}{2} = \frac{0}{2} = 0
\]

Thus, the midpoint \( M \) is:

\[
M = \left( \frac{3}{2}, 0 \right) \text{ or } (1.5, 0)
\]

So, the midpoint \( M \) of segment \( AB \) is \( (1.5, 0) \).