Question

the mid - point of $overline{rs}$ is $m(6,5)$. one endpoint is $s(5,10)$. find the coordinates of the other endpoint $r$. write the coordinates as decimals or integers.

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 $R=(x,y)$ and $S=(5,10)$ and $M=(6,5)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 5}{2}=6$. Multiply both sides by 2: $x + 5=12$. Then subtract 5 from both sides: $x=12 - 5=7$.

Step3: Solve for y - coordinate

We know that $\frac{y + 10}{2}=5$. Multiply both sides by 2: $y + 10 = 10$. Then subtract 10 from both sides: $y=10 - 10=0$.

Answer:

$(7,0)$