Question

Use the given endpoint R and midpoint of M of line RS to find the coordinates of the other endpoint S. R (4,-6), M (-7,8)

Answer 1

The coordinates of the midpoint are the arithmetic means of the respective coordinates of the endpoints.

The endpoints:

R(6,-2)

x₁=6

y₁=-2

S(x,y)

x₂=x

y₂=y

The midpoint:

M(5,3)

\begin{gathered}\frac{6+x}{2}=5 \\ 6+x=5 \times 2\\ 6+x=10 \\ x=10-6 \\ x=4 \\ \\ \frac{-2+y}{2}=3 \\ -2+y=3 \times 2 \\ -2+y=6 \\ y=6+2 \\ y=8\end{gathered}26+x=56+x=5×26+x=10x=10−6x=42−2+y=3−2+y=3×2−2+y=6y=6+2y=8

The coordinates of S are (4,8).