Question

The coordinates of point T are (0,6). The midpoint of ST is (4.-6). Find the coordinates

point S.

Answer 1

The coordinates of endpoint S are
`S(x,y) = (8,-18)`.

Explanation:

Let
`T(x, y) = (0, 6)` and
`M(x,y) = (4,-6)`, which is the midpoint of line segment ST. From Linear Algebra we get that midpoint is the following vector sum of endpoints S and T. That is:

`M(x,y) = (1)/(2)\cdot S(x,y) + (1)/(2)\cdot T(x,y)` (Eq. 1)

Now clear S in the previous expression:

`S(x,y) = 2\cdot M(x,y) - T(x,y)` (Eq. 1b)

Then, the coordinates of point S are:

`S(x,y) = 2\cdot (4,-6) - (0,6)`

`S(x,y) = (8, -18)`

The coordinates of endpoint S are
`S(x,y) = (8,-18)`.