Q is the midpoint of line segment PM. Find midpoint Q.

Question

Point P: (1, 2)
Point M: (1, -2)

Answer 1

To find the midpoint \( Q \) of the line segment \( PM \), we can use the midpoint formula. The formula for the midpoint \( Q(x, y) \) of two points \( P(x_1, y_1) \) and \( M(x_2, y_2) \) is given by:

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

Given:

• Point \( P(1, 2) \)
• Point \( M(1, -2) \)

Now, we can substitute the coordinates of points \( P \) and \( M \) into the formula:

1. Calculate the x-coordinate: \[ x = \frac{1 + 1}{2} = \frac{2}{2} = 1 \]

2. Calculate the y-coordinate: \[ y = \frac{2 + (-2)}{2} = \frac{2 - 2}{2} = \frac{0}{2} = 0 \]

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

\[ Q(1, 0) \]

The midpoint \( Q \) is \( (1, 0) \).