Answer
$$\color{blue}{(5,-4)}$$
Work Step by Step
To find the endpoint $B(x,y)$ when given the endpoint $A(19,16)$ and the midpoint $M(12,6)$ we will use the midpoint formula:
$${(\frac{x_{a}+x_{b}}{2},\frac{y_{a}+y_{b}}{2})}=M$$
$${(\frac{19+x_{b}}{2},\frac{16+y_{b}}{2})}=(12,6)$$
To find the $x$ value of $B$:
$\frac{19+x}{2}=12$
$19+x=24$
$x=5$
To find the $y$ value of $B$:
$\frac{16+y}{2}=6$
$16+y=12$
$y=-4$
So, the endpoint is at:
$$\color{blue}{(5,-4)}$$