Answer:
M(15, -6)
Step-by-step explanation:
The coordinates of the midpoint of a segment are the average of the coordinates of the endpoints. If we have the midpoint 'M(x_m, y_m)' and one endpoint 'Q(x_q, y_q)', we can find the coordinates of the other endpoint 'P(x_p, y_p)' using the midpoint formula:
[tex]\boxed{ \begin{array}{ccc} \text{\underline{Midpoint Formula:}} \\\\ M(x_m,y_m) = \left( \dfrac{x_p + x_q}{2}, \dfrac{y_p + y_q}{2} \right) \\\\ \text{Where:} \\ \bullet \ M(x_m,y_m) \ \text{is the midpoint} \\ \bullet \ (x_p, y_p) \ \text{and} \ (x_q, y_q) \ \text{are the coordinates of the endpoints} \end{array}}[/tex]
We are given:
[tex]\Longrightarrow M(5,-9) = \left( \dfrac{x_p +(-5)}{2}, \dfrac{y_p + (-12)}{2} \right)[/tex]
[tex]\Longrightarrow M(5,-9) = \left( \dfrac{x_p -5}{2}, \dfrac{y_p -12}{2} \right)[/tex]
Thus,
[tex]5 = \dfrac{x_p -5}{2} \text{ and } -9 = \dfrac{y_p -12}{2}[/tex]
Finding x_p:
[tex]\Longrightarrow 5 \cdot 2 = x_p -5\\\\\\\\\Longrightarrow x_p = 10+5\\\\\\\\\therefore x_p = 15[/tex]
Finding y_p:
[tex]\Longrightarrow -9 \cdot 2 = y_p -12\\\\\\\\\Longrightarrow y_p = -18+12\\\\\\\\\therefore y_p = -6[/tex]
Thus, the midpoint is (15, -6).