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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.
\(\text{Midpoint} = (\frac{x_1+x_2}{2}\), \(\frac{y_1+y_2}{2})\)
\(= (\frac{1 - 1}{2}\), \(\frac{1 - 1}{2})\)
\(= (\frac{0}{2}\), \(\frac{0}{2})\)
\(M = (0\), \(0)\)
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.
\(\text{Midpoint} = (\frac{x_1 + x_2}{2}\), \(\frac{y_1 + y_2}{2})\)
\(= (\frac{9 + 4}{2}\), \(\frac{2 + 3}{2})\)
\(M = (\frac{13}{2}\), \(\frac{5}{2})\)
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