Question

the midpoint m of rs has coordinates (8.5, 9). point s has coordinates (16, 5). 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 $S(16,5)$ and mid - point $M(8.5,9)$.

Step2: Solve for $x$

We know that $\frac{x + 16}{2}=8.5$. Multiply both sides by 2: $x + 16=17$. Then subtract 16 from both sides: $x=17 - 16=1$.

Step3: Solve for $y$

We know that $\frac{y + 5}{2}=9$. Multiply both sides by 2: $y + 5 = 18$. Then subtract 5 from both sides: $y=18 - 5 = 13$.

Answer:

$(1,13)$