Question

Find the missing endpoint if S is the midpoint RT. 1. R(9-4) and S(2,-1); find T

Answer 1

SOLUTION

We want to find the missing endpoint T in the line RT, given the point R(-9, 4) and the mid-point S(2, -1)

Since S is the mid-point, we will use the mid-point formula

$(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This becomes

$S(2,-1)=(\frac{-9+x_2}{2},\frac{4+y_2}{2})$

This follows that

$\begin{gathered} \frac{-9+x_2}{2}=2 \\ -9+x_2=4 \\ x_2=4+9 \\ x_2=13 \end{gathered}$

and

$\begin{gathered} \frac{4+y_2}{2}=-1 \\ 4+y_2=-2 \\ y_2=-2-4 \\ y_2=-6 \end{gathered}$

Hence the answer is

$T(13,-6)$