Hello, Ilsa!
Did you make a sketch?
$\displaystyle A, B, C$ are three collinear points.
$\displaystyle A$ and $\displaystyle B$ are (3,4) and (7,7), respectively,
and $\displaystyle AC$ is equal to 10 units.
Find the coordinates of $\displaystyle C.$ Code:
 C
 o
 * :
 * :3
 B * :
 (7,7)o        +
 * : 4
 * :3
 A * :
 (3,4)o        +
 4


 +                     

To go from point $\displaystyle A$ to point $\displaystyle B$, we move: right 4, up 3.
The length of $\displaystyle AB$ is: .$\displaystyle \sqrt{4^2+3^2} \:=\:\sqrt{25} \:=\:5$
Since the length of $\displaystyle AC$ is 10, then: .$\displaystyle BC = 5.$
To go from point $\displaystyle B$ to point $\displaystyle C$, we move (again): right 4, up 3.
Therefore, point C is at: .$\displaystyle (11,10)$