Question

The coordinates of point T are (0,4). the midpoint of ST is (7,-5). find the coordinates of point S

Answer 1

The formula of a midpoint:

`M_(ST)\left((x_S+x_T)/(2),\ (y_S+y_T)/(2)\right)`

We have:

`T(0,\ 4)\to x_T+0,\ y_T=4\\M(7,\ -5)\to x_M=7,\ y_M=-5`

Substitute:

`(x_S+0)/(2)=7\qquad|\cdot2\\\\x_S=14\\\\(y_S+4)/(2)=-5\qquad|\cdot2\\\\y_S+4=-10\qquad|-4\\\\y_S=-14`

Answer: S(14, -14).