Question

find the midpoint, m, of \\( \overline { a b } \\).
\\( a = ( - 5,1 ) b = ( 1, - 3 ) \\)
\\( m = ( ? , ) \\)
\\( m = ( \frac { x _ { 1 } + x _ { 2 } } { 2 } , \frac { y _ { 1 } + y _ { 2 } } { 2 } ) \\)

Explanation:

Step1: Identify coordinates

$x_1=-5,y_1 = 1,x_2=1,y_2=-3$

Step2: Calculate x - coordinate of mid - point

Use the formula $x=\frac{x_1 + x_2}{2}$.
Substitute values: $x=\frac{-5 + 1}{2}=\frac{-4}{2}=-2$

Step3: Calculate y - coordinate of mid - point

Use the formula $y=\frac{y_1 + y_2}{2}$.
Substitute values: $y=\frac{1+( - 3)}{2}=\frac{1 - 3}{2}=\frac{-2}{2}=-1$

Answer:

$(-2, -1)$