Question

Use the given endpoint R and midpoint M to line RS to find the coordinates of the other endpoint S. R(6,-2) M(5,3)

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)

$\frac{6+x}{2}=5 \\ 6+x=5 \times 2\\ 6+x=10 \\ x=10-6 \\ x=4 \\ \\ \frac{-2+y}{2}=3 \\ -2+y=3 \times 2 \\ -2+y=6 \\ y=6+2 \\ y=8$

The coordinates of S are (4,8).