Question

the coordinates of point t are (0,4). the midpoint of st is (4, - 8). find the coordinates of point s. the other endpoint is (square). (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 point $T=(x_2,y_2)=(0,4)$ and the mid - point $M=(4,-8)$. We want to find point $S=(x_1,y_1)$.

Step2: Solve for the x - coordinate of point S

Using the x - coordinate part of the mid - point formula $\frac{x_1 + x_2}{2}=M_x$. Substitute $x_2 = 0$ and $M_x=4$:
$\frac{x_1+0}{2}=4$, then $x_1=8$.

Step3: Solve for the y - coordinate of point S

Using the y - coordinate part of the mid - point formula $\frac{y_1 + y_2}{2}=M_y$. Substitute $y_2 = 4$ and $M_y=-8$:
$\frac{y_1 + 4}{2}=-8$. Multiply both sides by 2: $y_1+4=-16$. Then $y_1=-20$.

Answer:

$(8,-20)$