Question

the coordinates of point t are (0,4). the midpoint of $overline{st}$ is (4, - 8). 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 $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $S$ be $(x,y)$ and point $T=(0,4)$, and the mid - point $M=(4,-8)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 0}{2}=4$. Cross - multiply to get $x+0 = 8$, so $x = 8$.

Step3: Solve for y - coordinate

We know that $\frac{y + 4}{2}=-8$. Cross - multiply: $y + 4=-16$. Then subtract 4 from both sides: $y=-16 - 4=-20$.

Answer:

$(8,-20)$