Question

the coordinates of point t are (14,19). the mid - point of st is (7, - 9). 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 $(14,19)$, and the mid - point be $(7,-9)$.

Step2: Solve for the x - coordinate of point S

We have $\frac{x + 14}{2}=7$. Multiply both sides by 2: $x + 14=14$. Then subtract 14 from both sides: $x=0$.

Step3: Solve for the y - coordinate of point S

We have $\frac{y + 19}{2}=-9$. Multiply both sides by 2: $y + 19=-18$. Then subtract 19 from both sides: $y=-37$.

Answer:

$(0,-37)$