Question

The endpoints of AB are A(-3,-1) and B(5,1). What is the y-coordinate of the midpoint of AB?

Answer 1

To find the y-coordinate of the midpoint of a line segment with endpoints A(-3, -1) and B(5, 1), 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:

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

For points A and B, we have:
- \( A(x_1, y_1) = (-3, -1) \)
- \( B(x_2, y_2) = (5, 1) \)

Now, let's substitute the coordinates into the formula, focusing on the y-coordinate:

\[
y\text{-coordinate of } M = \frac{y_1 + y_2}{2} = \frac{-1 + 1}{2}
\]

Calculating this gives:

\[
\frac{-1 + 1}{2} = \frac{0}{2} = 0
\]

Therefore, the y-coordinate of the midpoint of AB is \( \boxed{0} \).