Answer:
P = (A +3B)/4
Step-by-step explanation:
A "directed" line segment is one that has a "beginning" and an "end". The first letter of the line segment's name is the beginning; the last letter is the end.
Line segment AB begins at point A and ends at point B.
The problem statement tells you what it means to locate point P so the segment is divided in the ratio 3:1.
AP : PB = 3 : 1
(P -A) / (B -P) = 3 / 1
P -A = 3(B -P) . . . . . . . . multiply by (B-P)
P +3P = A +3B . . . . . . . add A+3P
P = (A +3B)/4
You can find point P by filling in the coordinate values in the formula just found.
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<em>Comment on the general case</em>
If you derive the formula for P dividing the segment in the ratio m : n, you find it is ...
P = (nA +mB)/(m+n) . . . length ratios are applied in reverse to the end points
