Question

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

Answer 1

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)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

This becomes

`S(2,-1)=((-9+x_2)/(2),(4+y_2)/(2))`

This follows that

`\begin{gathered} (-9+x_2)/(2)=2 \\ -9+x_2=4 \\ x_2=4+9 \\ x_2=13 \end{gathered}`

and

`\begin{gathered} (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)`