Question

find the midpoint, m, of \\( \overline { a b } \\).
\\( a = ( 2,5 ) b = ( - 6, - 3 ) \\)
\\( m = ( ? , \square ) \\)
\\( m = ( \frac { x _ { 1 } + x _ { 2 } } { 2 } , \frac { y _ { 1 } + y _ { 2 } } { 2 } ) \\)

Explanation:

Step1: Substitute coordinates into midpoint formula

Given \(A=(x_1,y_1)=(2,5)\) and \(B=(x_2,y_2)=(-6,-3)\), use the midpoint formula \(M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
So, \(x\) - coordinate: \(\frac{2+(-6)}{2}\), \(y\) - coordinate: \(\frac{5+(-3)}{2}\).

Step2: Calculate \(x\) - coordinate

\(\frac{2+(-6)}{2}=\frac{2 - 6}{2}=\frac{-4}{2}=-2\).

Step3: Calculate \(y\) - coordinate

\(\frac{5+(-3)}{2}=\frac{5 - 3}{2}=\frac{2}{2}=1\).

Answer:

$(-2,1)$