Question

The midpoint of a line segment is (1,5). if one endpoint is (4,7), what is the ither endpoint?​

Answer 1

Let

$A=(A_x, A_y),\quad M=(1,5), B=(4,7)$

By definition, the coordinates of the midpoint are the average of the coordinates of the endpoints:

$M_x=\left(\dfrac{A_x+B_x}{2}\right),\quad M_y=\left(\dfrac{A_y+B_y}{2}\right)$

We deduce, solving for the coordinates of A:

$A_x=2M_x-B_x,\quad A_y=2M_y-B_y$

Plug your values:

$A_x=2\cdot 1-4,\quad A_y=2\cdot 5-7$

Which evaluates to

$A_x=-2,\quad A_y=3$