Question

Find the midpoint M of the line segment jolning the points P = (-7, - 5) and Q = (5, - 1).

Answer 1

To find the midpoint \( M \) of the line segment joining the points \( P = (-7, -5) \) and \( Q = (5, -1) \), we use the midpoint formula:

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

Here, \( (x_1, y_1) = (-7, -5) \) and \( (x_2, y_2) = (5, -1) \).

Now, we can calculate the coordinates of the midpoint \( M \):

1. Calculate the x-coordinate of \( M \):
\[
\frac{x_1 + x_2}{2} = \frac{-7 + 5}{2} = \frac{-2}{2} = -1
\]

2. Calculate the y-coordinate of \( M \):
\[
\frac{y_1 + y_2}{2} = \frac{-5 + (-1)}{2} = \frac{-5 - 1}{2} = \frac{-6}{2} = -3
\]

Thus, the midpoint \( M \) is given by:

\[
M = (-1, -3)
\]

In conclusion, the midpoint of the line segment joining the points \( P \) and \( Q \) is \( M = (-1, -3) \).