Question

If a line segment contains one endpoint at (2,3) and has a midpoint of (-2,6) what is the second endpoint of the line segment

Answer 1

Explanation:

The coordinates of the midpoint M are the average of the coordinates of the two endpoints:

`M_x = (2+x)/(2),\quad M_y = (3+y)/(2)`

Plug the known coordinates of the midpoint:

`-2 = (2+x)/(2),\quad 6 = (3+y)/(2)`

Solve for x and y:

`-4 = 2+x,\quad 12 = 3+y`

`x=-6,\quad y = 9`