Question

rs has a midpoint at m(4, 9). point s is at (3, 8). 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 $R=(x,y)$ and $S=(3,8)$ and $M=(4,9)$.

Step2: Solve for x - coordinate of R

We know that $\frac{x + 3}{2}=4$. Multiply both sides by 2: $x + 3=8$. Then subtract 3 from both sides: $x=8 - 3=5$.

Step3: Solve for y - coordinate of R

We know that $\frac{y + 8}{2}=9$. Multiply both sides by 2: $y + 8=18$. Then subtract 8 from both sides: $y=18 - 8 = 10$.

Answer:

$(5,10)$