Finding points on a line with a given distance

Start point - (x0, y0)

End point - (x1, y1)

We need to find a point (xt, yt) at a distance dt from start point towards end point.

The distance between Start and End point is given by d = sqrt((x1 - x0)^2 + (y1 - y0)^2)

Let the ratio of distances, t = dt / d

Then the point (xt, yt) = (((1 - t) * x0 + t * x1), ((1 - t) * y0 + t * y1))

When 0 < t < 1, the point is on the line.

When t < 0, the point is outside the line near to (x0, y0).

When t > 1, the point is outside the line near to (x1, y1).