Question

Show all work and provide necessary descriptions

Answer 1

Let

`P=(P_x,P_y),\quad Q=(Q_x,Q_y)`

If M is the midpoint, the x and y coordinates of M are the average of the x and y coordinates of P and Q:

`M=\left((P_x+Q_x)/(2),\ (P_y+Q_y)/(2)\right)`

We can solve this expression for the coordinates of Q:

`M_x = (P_x+Q_x)/(2) \implies Q_x = 2M_x-P_x`

`M_y = (P_y+Q_y)/(2) \implies Q_y = 2M_y-P_y`

Plug in the values for the coordinates of M and P to get

`Q_x = 2M_x-P_x = 2\cdot 5-11 = 10-11=-1`

`Q_y = 2M_y-P_y = 2\cdot (-2) - (-10) = -4+10=6`