Find the coordinates of p so that p partitions the segment AB in the ratio 3:1 if A(0,7) and B(-4,2)

Question

A. (-3, -3.75)

B. (-5,-4)

C. (-3,-10.75)

D. (-3, 3.25)

Answer 1

The new point will be (xp , yp) where p stands for partition. So xp = x1 + 3/(3+1)*(x2-x1) and yp = y1 + 3/(3+1)*(y2-y1).

for the x coordinate, you will do: 0 + 3/(3+1)x(-4-0)

for the y coordinate, you will do: 7 + 3/(3+1)x(2-7)

which give the answer as: (xp , yp) = (-3, 3.25) D

Answer 2

If the segment is split in a ratio of 3:1, that means there are 4 equal segments. If there are 4 equal segments, then the middle point (2nd point) is the midpoint of the segment, let's call it point M. Then the point p in question is the midpoint of either AM or MB. Let's pick AM.

Point M is located at x = (0 + -4)/2 or x = -2 and y = (7 + 2)/2 or y = 4.5. So M(-2, 4.5).

Point p would then be located at x = (0 + -1)/2 or x = -1 and y = (7 + 4.5)/2 or y = 5,75 so p(-1, 5.75)