Question

the midpoint of $overline{rs}$ is $m(11.35, 6.75)$. one endpoint is $s(7.4, 10.9)$. find the coordinates of the other endpoint $r$. write the coordinates as decimals or integers. $r=(spacespace,spacespace)$

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 $S=(7.4,10.9)$ and $M=(11.35,6.75)$.

Step2: Solve for x - coordinate of R

We know that $\frac{x + 7.4}{2}=11.35$. Multiply both sides by 2: $x + 7.4=2\times11.35$. Then $x+7.4 = 22.7$. Subtract 7.4 from both sides: $x=22.7−7.4=15.3$.

Step3: Solve for y - coordinate of R

We know that $\frac{y + 10.9}{2}=6.75$. Multiply both sides by 2: $y + 10.9=2\times6.75$. Then $y + 10.9=13.5$. Subtract 10.9 from both sides: $y=13.5−10.9 = 2.6$.

Answer:

$(15.3,2.6)$