Question

rs has a midpoint at m(20.5, 18.5). point r is at (38, -26). 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 $R(x_1,y_1)=(38,-26)$ and $S(x_2,y_2)$. The mid - point $M(20.5,18.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=20.5$. Substitute $x_1 = 38$ into the equation: $\frac{38+x_2}{2}=20.5$. Multiply both sides by 2: $38 + x_2=41$. Then subtract 38 from both sides: $x_2=41 - 38=3$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=18.5$. Substitute $y_1=-26$ into the equation: $\frac{-26 + y_2}{2}=18.5$. Multiply both sides by 2: $-26+y_2 = 37$. Then add 26 to both sides: $y_2=37 + 26=63$.

Answer:

$(3,63)$