# Question #5c7c6

$\left(7 , 3\right)$
The line segment is $14$ units long, and we need to split this into two segments with lengths in the ratio $3 : 4$.
Hence, we know that the first line segment is going to be $\frac{3}{7}$ the length of the original line, and the second will be $\frac{4}{7}$ of that original length. Applying this ratio to the line of length 14, we know that the first segment will be 6 units long, and the second 8 units long.
The line is parallel to the $x$ axis so we do not need to account for changes in $y$. Since the leftmost point on the line is $\left(1 , 3\right)$, it follows trivially that the dividing point will be $\left(1 + 6 , 3\right)$, or $\left(7 , 3\right)$.