To find the midpoint [tex]\( M \)[/tex] of a line segment with endpoints [tex]\( J \)[/tex] and [tex]\( K \)[/tex], we use the midpoint formula. The midpoint formula for a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints [tex]\( J(-18, -18) \)[/tex] and [tex]\( K(-4, 0) \)[/tex]:
1. Identify the coordinates of the endpoints:
- [tex]\( J \)[/tex] has coordinates [tex]\( (x_1, y_1) = (-18, -18) \)[/tex].
- [tex]\( K \)[/tex] has coordinates [tex]\( (x_2, y_2) = (-4, 0) \)[/tex].
2. Plug these coordinates into the midpoint formula:
- For the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{-18 + (-4)}{2} = \frac{-18 - 4}{2} = \frac{-22}{2} = -11.0
\][/tex]
- For the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{-18 + 0}{2} = \frac{-18}{2} = -9.0
\][/tex]
3. Combine the x and y coordinates to get the midpoint [tex]\( M \)[/tex]:
[tex]\[
M = (-11.0, -9.0)
\][/tex]
Thus, the midpoint [tex]\( M \)[/tex] of the line segment with endpoints [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is:
[tex]\[ M = (-11.0, -9.0) \][/tex]
