Answer
$$\color{blue}{(-3,6)}$$
Work Step by Step
To find the endpoint $B(x,y)$ when given the endpoint $A(13,10)$ and the midpoint $M(5,8)$ we will use the midpoint formula:
$${(\frac{x_{a}+x_{b}}{2},\frac{y_{a}+y_{b}}{2})}=M$$
$${(\frac{13+x_{b}}{2},\frac{10+y_{b}}{2})}=(5,8)$$
To find the $x$ value of $B$:
$\frac{13+x}{2}=5$
$13+x=10$
$x=-3$
To find the $y$ value of $B$:
$\frac{10+y}{2}=8$
$10+y=16$
$y=6$
So, the endpoint is at:
$$\color{blue}{(-3,6)}$$
