Question

the midpoint m of $overline{rs}$ has coordinates (40.5, 27.5). point s has coordinates (80, 49). 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 point $S=(80,49)$ and mid - point $M=(40.5,27.5)$.

Step2: Solve for $x$

We know that $\frac{x + 80}{2}=40.5$. Multiply both sides by 2: $x + 80=40.5\times2=81$. Then subtract 80 from both sides: $x=81 - 80=1$.

Step3: Solve for $y$

We know that $\frac{y + 49}{2}=27.5$. Multiply both sides by 2: $y + 49=27.5\times2 = 55$. Then subtract 49 from both sides: $y=55 - 49 = 6$.

Answer:

$(1,6)$