Question

find the midpoint, m, of \\( \overline { a b } \\).
\\( a = ( 10,1 ) b = ( - 6,3 ) \\)
\\( m = ( \square, \square ) \\)
\\( m = ( \frac { x _ { 1 } + x _ { 2 } } { 2 }, \frac { y _ { 1 } + y _ { 2 } } { 2 } ) \\)

Explanation:

Step1: Calculate the x - coordinate of the midpoint

Use the formula for the x - coordinate of the midpoint \(x=\frac{x_1 + x_2}{2}\). Here \(x_1 = 10\) and \(x_2=-6\).

$$x=\frac{10+( - 6)}{2}=\frac{10 - 6}{2}=\frac{4}{2}=2$$

Step2: Calculate the y - coordinate of the midpoint

Use the formula for the y - coordinate of the midpoint \(y=\frac{y_1 + y_2}{2}\). Here \(y_1 = 1\) and \(y_2 = 3\).

$$y=\frac{1+3}{2}=\frac{4}{2}=2$$

Answer:

\((2,2)\)