Question

Find the midpoint of AB in the rectangle ABCD with vertices A (0, 0), B (a, 0), C (a, b), and D (0, b).

Answer 1

To find the midpoint of the line segment AB in the rectangle ABCD with vertices A (0, 0) and B (a, 0), we can use the midpoint formula. The midpoint M of a segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

In our case, the coordinates of point A are \((0, 0)\) and the coordinates of point B are \((a, 0)\). Plugging these coordinates into the midpoint formula:

1. Identify the coordinates:
- \(A(x_1, y_1) = (0, 0)\)
- \(B(x_2, y_2) = (a, 0)\)

2. Apply the midpoint formula:
- Midpoint \(M\) coordinates:
\[
M = \left(\frac{0 + a}{2}, \frac{0 + 0}{2}\right) = \left(\frac{a}{2}, 0\right)
\]

Therefore, the midpoint of segment AB is:

\[
\boxed{\left(\frac{a}{2}, 0\right)}
\]