Question

the mid - point n of $overline{rs}$ has coordinates $(10.5,3.5)$. point s has coordinates $(5,6)$. find the coordinates of point r. write the coordinates as decimals or integers. r = ( , )

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 the coordinates of point $R$ be $(x,y)$ and the coordinates of point $S$ be $(5,6)$ and the mid - point $N$ be $(10.5,3.5)$.

Step2: Solve for $x$

For the $x$ - coordinate of the mid - point: $\frac{x + 5}{2}=10.5$. Multiply both sides by 2: $x + 5=21$. Subtract 5 from both sides: $x=21 - 5=16$.

Step3: Solve for $y$

For the $y$ - coordinate of the mid - point: $\frac{y + 6}{2}=3.5$. Multiply both sides by 2: $y+6 = 7$. Subtract 6 from both sides: $y=7 - 6 = 1$.

Answer:

$(16,1)$