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:

$M_{ST}\left(\dfrac{x_S+x_T}{2},\ \dfrac{y_S+y_T}{2}\right)$

We have:

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

Substitute:

$\dfrac{x_S+0}{2}=7\qquad|\cdot2\\\\x_S=14\\\\\dfrac{y_S+4}{2}=-5\qquad|\cdot2\\\\y_S+4=-10\qquad|-4\\\\y_S=-14$

Answer: S(14, -14).