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 for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve for 10.

Let $R(-9,4)$ and $S(2,-1)$. Let $T(x,y)$. Then $\frac{-9 + x}{2}=2$ and $\frac{4 + y}{2}=-1$. Solving for $x$: $-9+x = 4$, so $x = 13$. Solving for $y$: $4 + y=-2$, so $y=-6$. So $T(13,-6)$.

Step3: Solve for 11.

Let $S(-4,-6)$ and $T(-7,-3)$. Let $R(x,y)$. Then $\frac{x-7}{2}=-4$ and $\frac{y - 3}{2}=-6$. Solving for $x$: $x-7=-8$, so $x=-1$. Solving for $y$: $y-3=-12$, so $y=-9$. So $R(-1,-9)$.

Answer:

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