Line segment ab has endpoints a(1, 4) and b(4, 2). find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1: 4.

For this case we have the following expression for AB:
 ((x2-x1), (y2-y1))
 Substituting values:
 ((4-1), (2-4))
 (3, -2)
 For AX we have:
 (3 * (1/4), -2 * (1/4))
 Rewriting:
 (3/4, -1/2)
 Then, the coordinates of point x are:
 ((1 + 3/4), (4 - 1/2))
 ((1 + 3/4), (4 - 1/2))
 (7/4, 7/2)
 
 the coordinates of the point that divides the line segment directed from A to B in the ratio of 1: 4 is:
 (7/4, 7/2)

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.