Question

the midpoint of st is m = (-1, 6). one endpoint is s = (3, 4). find the coordinates of the other endpoint, t.

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 $S=(x_1,y_1)=(3,4)$ and $T=(x_2,y_2)$ and $M=(-1,6)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-1$. Substitute $x_1 = 3$ into the equation: $\frac{3+x_2}{2}=-1$. Multiply both sides by 2: $3 + x_2=-2$. Then subtract 3 from both sides: $x_2=-2 - 3=-5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=6$. Substitute $y_1 = 4$ into the equation: $\frac{4+y_2}{2}=6$. Multiply both sides by 2: $4 + y_2 = 12$. Then subtract 4 from both sides: $y_2=12 - 4 = 8$.

Answer:

$(-5,8)$