Getting the coordinates of a point on section

Question

What is the endpoint $P(x,y)$ of a line segment , if I know its starting point: $C(x(1), y(1))$, the gradient $G$, and its length $L$?

Answer 1

HINT:

$$(x-x_1)^2+(y-y_1)^2=L^2$$

and $$G=\dfrac{y-y_1}{x-x_1}$$

Answer 2

$$ D = C + L (G/\lVert G\rVert) $$ where $$ \lVert G\rVert= \sqrt{\sum_{i=1}^2 G_i^2} $$ is the length of $G$.