To find the coordinates of the midpoint of a line segment joining two points, we can use the midpoint formula. The midpoint formula is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
Given points are:
[tex]\[
(5, 9) \quad \text{and} \quad (1, -1)
\][/tex]
Let's apply the midpoint formula step by step:
1. Identify [tex]\(x_1\)[/tex], [tex]\(y_1\)[/tex], [tex]\(x_2\)[/tex], and [tex]\(y_2\)[/tex]:
[tex]\[
x_1 = 5, \quad y_1 = 9, \quad x_2 = 1, \quad y_2 = -1
\][/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{5 + 1}{2} = \frac{6}{2} = 3
\][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{9 + (-1)}{2} = \frac{9 - 1}{2} = \frac{8}{2} = 4
\][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[
(3.0, 4.0)
\][/tex]
Thus, the midpoint of the line segment joining the points [tex]\((5, 9)\)[/tex] and [tex]\((1, -1)\)[/tex] is [tex]\((3, 4)\)[/tex].
