Question

the coordinates of point t are (0,2). the midpoint of st is (6, - 7). 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 $T=(x_1,y_1)=(0,2)$ and the mid - point $M=(6,-7)$. Let the coordinates of point $S=(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=6$. Substitute $x_1 = 0$ into the equation: $\frac{0 + x_2}{2}=6$, which simplifies to $\frac{x_2}{2}=6$. Multiply both sides by 2 to get $x_2=12$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-7$. Substitute $y_1 = 2$ into the equation: $\frac{2 + y_2}{2}=-7$. Multiply both sides by 2: $2 + y_2=-14$. Subtract 2 from both sides: $y_2=-14 - 2=-16$.

Answer:

$(12,-16)$