Sure, let's find the midpoint of the segment between the points [tex]\((15, 3)\)[/tex] and [tex]\((2, -14)\)[/tex].
To find the midpoint of a line segment, you can use the midpoint formula:
[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 endpoints of the segment.
Here, the coordinates given are:
[tex]\[
(x_1, y_1) = (15, 3)
\][/tex]
[tex]\[
(x_2, y_2) = (2, -14)
\][/tex]
Substitute the coordinates into the midpoint formula:
[tex]\[
\left( \frac{15 + 2}{2}, \frac{3 + (-14)}{2} \right) = \left( \frac{17}{2}, \frac{-11}{2} \right)
\][/tex]
Simplify the expressions inside the parentheses:
[tex]\[
\left( \frac{17}{2}, \frac{-11}{2} \right)
\][/tex]
Thus, the midpoint of the segment between the points [tex]\((15, 3)\)[/tex] and [tex]\((2, -14)\)[/tex] is:
[tex]\[
\left( \frac{17}{2}, \frac{-11}{2} \right)
\][/tex]
So, the correct answer is:
[tex]\[
B. \left( \frac{17}{2}, \frac{-11}{2} \right)
\][/tex]
