Question

the coordinates of point t are (0,6). the midpoint of st is (3, - 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 $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $T=(x_T,y_T)=(0,6)$ and the mid - point $M=(x_M,y_M)=(3,-7)$, and the coordinates of point $S=(x_S,y_S)$.

Step2: Solve for $x_S$

We know that $x_M=\frac{x_T + x_S}{2}$. Substituting the known values: $3=\frac{0 + x_S}{2}$. Multiply both sides by 2: $6 = 0+x_S$, so $x_S=6$.

Step3: Solve for $y_S$

We know that $y_M=\frac{y_T + y_S}{2}$. Substituting the known values: $-7=\frac{6 + y_S}{2}$. Multiply both sides by 2: $-14=6 + y_S$. Subtract 6 from both sides: $y_S=-14 - 6=-20$.

Answer:

$(6,-20)$