Question

the midpoint of $overline{st}$ is $m=(3, 1)$. one endpoint is $s=(1, - 2)$. 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 $S=(x_1,y_1)=(1,-2)$ and $T=(x_2,y_2)$ and $M=(3,1)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=3$. Substitute $x_1 = 1$ into the equation: $\frac{1+x_2}{2}=3$. Multiply both sides by 2: $1 + x_2=6$. Then subtract 1 from both sides: $x_2=6 - 1=5$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=1$. Substitute $y_1=-2$ into the equation: $\frac{-2 + y_2}{2}=1$. Multiply both sides by 2: $-2+y_2=2$. Then add 2 to both sides: $y_2=2 + 2=4$.

Answer:

$(5,4)$