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 $R=(x_1,y_1)=(12,13)$ and $S=(x_2,y_2)$, and $M=(1,16)$.

Step2: Solve for the x - coordinate of S

We know that $\frac{x_1 + x_2}{2}=1$. Substitute $x_1 = 12$ into the equation: $\frac{12+x_2}{2}=1$. Multiply both sides by 2: $12 + x_2=2$. Then subtract 12 from both sides: $x_2=2 - 12=-10$.

Step3: Solve for the y - coordinate of S

We know that $\frac{y_1 + y_2}{2}=16$. Substitute $y_1 = 13$ into the equation: $\frac{13+y_2}{2}=16$. Multiply both sides by 2: $13 + y_2=32$. Then subtract 13 from both sides: $y_2=32 - 13 = 19$.

Answer:

$(-10,19)$