To find the midpoint of a line segment between two points, we use the midpoint formula. The formula for the midpoint [tex]\( M \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula step-by-step for the given points [tex]\((17, 1)\)[/tex] and [tex]\((-2, 8)\)[/tex]:
1. Identify the coordinates of the points:
- First point: [tex]\((x_1, y_1) = (17, 1)\)[/tex]
- Second point: [tex]\((x_2, y_2) = (-2, 8)\)[/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{17 + (-2)}{2} = \frac{15}{2} = 7.5
\][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{1 + 8}{2} = \frac{9}{2} = 4.5
\][/tex]
4. Combine the x and y coordinates to find the midpoint:
[tex]\[
M = \left( 7.5, 4.5 \right)
\][/tex]
Therefore, the midpoint of the segment between the points [tex]\((17, 1)\)[/tex] and [tex]\((-2, 8)\)[/tex] is [tex]\(\left( \frac{15}{2}, \frac{9}{2} \right)\)[/tex].
So, the correct answer is:
D. [tex]\(\left( \frac{15}{2}, \frac{9}{2} \right)\)[/tex]
