Question

the coordinates of point t are (10,15). the midpoint of \overline{st} is (5, -8). find the coordinates of point s. the other endpoint is \square. (type an ordered pair.)

Explanation:

Step1: Recall midpoint formula

The midpoint $M=(x_m,y_m)$ of segment $\overline{ST}$ with endpoints $S=(x_s,y_s)$ and $T=(x_t,y_t)$ is given by:
$$x_m=\frac{x_s+x_t}{2}, \quad y_m=\frac{y_s+y_t}{2}$$

Step2: Isolate $x_s$ and solve

Rearrange the x-coordinate formula to solve for $x_s$:
$$x_s=2x_m - x_t$$
Substitute $x_m=5$, $x_t=10$:
$$x_s=2(5)-10=10-10=0$$

Step3: Isolate $y_s$ and solve

Rearrange the y-coordinate formula to solve for $y_s$:
$$y_s=2y_m - y_t$$
Substitute $y_m=-8$, $y_t=15$:
$$y_s=2(-8)-15=-16-15=-31$$

Answer:

$(0, -31)$