Question

the midpoint of $overline{st}$ is $m=(3,5)$. one endpoint is $s=(5,8)$. 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 $S=(x_1,y_1)=(5,8)$ and $T=(x_2,y_2)$ and $M=(3,5)$.

Step2: Solve for $x_2$

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

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substitute $y_1 = 8$ and $y_M = 5$ into the formula: $\frac{8 + y_2}{2}=5$. Multiply both sides by 2: $8 + y_2=10$. Then subtract 8 from both sides: $y_2=10 - 8 = 2$.

Answer:

$(1,2)$