Question

The coordinates of point T are (6, 14). The midpoint of ST is (3, -10). Find the coordinates of point S

Answer 1

Answer: S(0,-34)

Explanation:

`\displaystyle\\The\ midpoint \ Q_x=(x_S+x_T)/(2) \\\\Q_x=(x_S+x_T)/(2)\\`

Multiply both parts of the equation by 2:

`2Q_x=x_S+x_T\\2Q_x-x_T=x_S+x_T-x_T\\2Q_x-x_T=x_S\\x_S=2Q_x-x_T\\Hence,\\Q(3,-10)\ \ \ \ T(6,14)\\x_S=2*3-6\\x_S=6-6\\x_S=0\\Similarly:\\y_S=2Q_y-y_T\\y_S=2*(-10)-14\\y_S=-20-14\\y_S=-34\\Thus,\\S(0,-34)`