Question

find the midpoint, m, of \\(\overline{ab}\\). \\(a = (2, 5)\\) \\(b = (-6, -3)\\) \\(m = (?, \\ )\\) \\(m = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \
ight)\\)

Explanation:

Step1: Identify coordinates

Let \( A=(x_1,y_1)=(2,5) \) and \( B=(x_2,y_2)=(-6,-3) \).

Step2: Calculate x - coordinate of midpoint

Using the midpoint formula for x - coordinate: \( \frac{x_1 + x_2}{2} \).
Substitute \( x_1 = 2 \) and \( x_2=-6 \): \( \frac{2+(-6)}{2}=\frac{2 - 6}{2}=\frac{-4}{2}=-2 \).

Step3: Calculate y - coordinate of midpoint

Using the midpoint formula for y - coordinate: \( \frac{y_1 + y_2}{2} \).
Substitute \( y_1 = 5 \) and \( y_2=-3 \): \( \frac{5+(-3)}{2}=\frac{5 - 3}{2}=\frac{2}{2}=1 \).

Answer:

\( M = (-2,1) \)