Question

the midpoint m of $overline{rs}$ has coordinates $(5, 14.5)$. point r has coordinates $(10, 10)$. 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 $R=(x_1,y_1)=(10,10)$ and $S=(x_2,y_2)$, and $M=(5,14.5)$.

Step2: Find the x - coordinate of point S

We know that $\frac{x_1 + x_2}{2}=5$, substituting $x_1 = 10$ into the equation: $\frac{10+x_2}{2}=5$. Multiply both sides by 2: $10 + x_2=10$, then $x_2=0$.

Step3: Find the y - coordinate of point S

We know that $\frac{y_1 + y_2}{2}=14.5$, substituting $y_1 = 10$ into the equation: $\frac{10 + y_2}{2}=14.5$. Multiply both sides by 2: $10+y_2 = 29$, then $y_2=19$.

Answer:

$(0,19)$