Question

find the midpoint, m, of \\( \overline { a b } \\).
\\( a = ( - 2, - 10 ) \\) \\( b = ( - 6,0 ) \\)
\\( m = ( \text { ? } , ) \\)
\\( m = \left( \frac { x _ { 1 } + x _ { 2 } } { 2 } , \frac { y _ { 1 } + y _ { 2 } } { 2 } \
ight) \\)

Explanation:

Step1: Calculate the x - coordinate of the midpoint

Use the formula \(x=\frac{x_1 + x_2}{2}\), where \(x_1=-2\) and \(x_2=-6\).
\(x=\frac{-2+(-6)}{2}=\frac{-2 - 6}{2}=\frac{-8}{2}=-4\)

Step2: Calculate the y - coordinate of the midpoint

Use the formula \(y=\frac{y_1 + y_2}{2}\), where \(y_1=-10\) and \(y_2 = 0\).
\(y=\frac{-10 + 0}{2}=\frac{-10}{2}=-5\)

Answer:

\((-4,-5)\)