Question

directions: find the missing endpoint if s is the midpoint $overline{rt}$. 10. $r(-9,4)$ and $s(2,-1)$; find $t$. 11. $s(-4,-6)$ and $t(-7,-3)$; find $r$.

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of $R=(x_R,y_R)$, $S=(x_S,y_S)$ and $T=(x_T,y_T)$.

Step2: Solve for $x$ and $y$ of the missing point in problem 10

Given $R(-9,4)$ and $S(2,-1)$. For the $x$ - coordinate: $\frac{-9+x_T}{2}=2$. Cross - multiply: $-9 + x_T=4$, then $x_T=4 + 9=13$. For the $y$ - coordinate: $\frac{4+y_T}{2}=-1$. Cross - multiply: $4 + y_T=-2$, then $y_T=-2 - 4=-6$. So $T=(13,-6)$.

Step3: Solve for $x$ and $y$ of the missing point in problem 11

Given $S(-4,-6)$ and $T(-7,-3)$. For the $x$ - coordinate: $\frac{x_R-7}{2}=-4$. Cross - multiply: $x_R-7=-8$, then $x_R=-8 + 7=-1$. For the $y$ - coordinate: $\frac{y_R-3}{2}=-6$. Cross - multiply: $y_R-3=-12$, then $y_R=-12 + 3=-9$. So $R=(-1,-9)$.

Answer:

1. $T=(13,-6)$
2. $R=(-1,-9)$