Question

directions: find the missing endpoint if s is the mid - point rt. 10. r(-9, 4) and s(2, -1); find t.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $R(-9,4)$ be $(x_1,y_1)$ and $T(x,y)$ be $(x_2,y_2)$, and $S(2,-1)$ be the mid - point.

Step2: Solve for the x - coordinate of T

We have $\frac{-9 + x}{2}=2$. Multiply both sides by 2: $-9 + x = 4$. Then add 9 to both sides: $x=4 + 9=13$.

Step3: Solve for the y - coordinate of T

We have $\frac{4 + y}{2}=-1$. Multiply both sides by 2: $4 + y=-2$. Then subtract 4 from both sides: $y=-2 - 4=-6$.

Answer:

$T(13,-6)$