Question

the midpoint m of rs has coordinates (1, 16). point r has coordinates (12, 13). find the coordinates of point s. write the coordinates as decimals or integers. s =

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 $S$ be $(x,y)$, $R=(12,13)$ and $M=(1,16)$.

Step2: Solve for x - coordinate of S

We know that $\frac{12 + x}{2}=1$. Multiply both sides by 2: $12 + x=2$. Then subtract 12 from both sides: $x=2 - 12=-10$.

Step3: Solve for y - coordinate of S

We know that $\frac{13 + y}{2}=16$. Multiply both sides by 2: $13 + y=32$. Then subtract 13 from both sides: $y=32 - 13 = 19$.

Answer:

$(-10,19)$