Theory:

Problem \(1\):
 
Find the mid-point of the vertices \(A(1\), \(1)\) and \(B(-1\), \(-1)\).
 
Given:
 
The end points of the line segment are \(A(1\), \(1)\) and \(B(-1\), \(-1)\).
 
\(x_1 = 1\)
 
\(x_2 = -1\)
 
\(y_1 = 1\)
 
\(y_2 = -1\)
 
Let \(M\) be the mid-point of the line segment.
 
Figure_5.svg
 
\(\text{Midpoint} = (\frac{x_1+x_2}{2}\), \(\frac{y_1+y_2}{2})\)
 
\(= (\frac{1 - 1}{2}\), \(\frac{1 - 1}{2})\)
 
\(= (\frac{0}{2}\), \(\frac{0}{2})\)
 
\(M = (0\), \(0)\)
 
 
Problem \(2\):
 
Find the mid-point of the vertices \(A(9\), \(2)\) and \(B(4\), \(5)\).
 
Given:
 
The end points of the line segment are \(A(9\), \(2)\) and \(B(4\), \(3)\).
 
\(x_1 = 9\)
 
\(x_2 = 4\)
 
\(y_1 = 2\)
 
\(y_2 = 3\)
 
Let \(M\) be the mid-point of the line segment.
 
Figure_6.svg
 
\(\text{Midpoint} = (\frac{x_1 + x_2}{2}\), \(\frac{y_1 + y_2}{2})\)
 
\(= (\frac{9 + 4}{2}\), \(\frac{2 + 3}{2})\)
 
\(M = (\frac{13}{2}\), \(\frac{5}{2})\)