AR:AB = 1/5 means that AR has length equal to 1/5 of the length of AB.
To find the x coordinate of R, you take 4/5 of the x coordinate of A plus 1/5 of the x coordinate of B:
4/5 * 1 + 1/5 * 4 = 8/5
You do the same for the y coordinate:
4/5 * (-1) + 1/5 * 4 = 0
So the point R has coordinates (8/5, 0).
