To find the midpoint of the segment between the points [tex]\((15, 3)\)[/tex] and [tex]\((2, -14)\)[/tex], we use the midpoint formula. The midpoint [tex]\((M_x, M_y)\)[/tex] of a segment connecting two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
M_x = \frac{x_1 + x_2}{2}
\][/tex]
[tex]\[
M_y = \frac{y_1 + y_2}{2}
\][/tex]
Let's apply these formulas step-by-step:
1. Identify the coordinates of the points:
- [tex]\((x_1, y_1) = (15, 3)\)[/tex]
- [tex]\((x_2, y_2) = (2, -14)\)[/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[
M_x = \frac{15 + 2}{2}
\][/tex]
[tex]\[
M_x = \frac{17}{2}
\][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[
M_y = \frac{3 + (-14)}{2}
\][/tex]
[tex]\[
M_y = \frac{3 - 14}{2}
\][/tex]
[tex]\[
M_y = \frac{-11}{2}
\][/tex]
Thus, the midpoint of the segment is:
[tex]\[
\left(\frac{17}{2}, -\frac{11}{2}\right)
\][/tex]
Comparing this with the given options, the correct answer is:
C. [tex]\(\left(\frac{17}{2}, -\frac{11}{2}\right)\)[/tex]
