Question

the coordinates of point t are (0,5). the mid - point of $overline{st}$ is (6, - 5). find the coordinates of point s. the other endpoint is . (type an ordered pair.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $S$ be $(x,y)$ and the coordinates of point $T$ be $(0,5)$, and the mid - point be $(6,-5)$.

Step2: Solve for $x$

We have $\frac{x + 0}{2}=6$. Cross - multiply: $x+0 = 12$, so $x = 12$.

Step3: Solve for $y$

We have $\frac{y + 5}{2}=-5$. Cross - multiply: $y + 5=-10$. Then subtract 5 from both sides: $y=-10 - 5=-15$.

Answer:

$(12,-15)$