Question

the coordinates of point t are (0,3). the mid - point of st is (2, - 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 the coordinates of point $T$ be $(0,3)$, and the mid - point of $\overline{ST}$ be $(2,-8)$.

Step2: Solve for $x$

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

Step3: Solve for $y$

We have $\frac{y + 3}{2}=-8$. Cross - multiply: $y + 3=-16$. Then subtract 3 from both sides: $y=-16 - 3=-19$.

Answer:

$(4,-19)$