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Answer:
use the formula B = (P +2A)/3
Step-by-step explanation:
Suppose point B is the point that does the division. The problem statement tells you that B is located such that ...
AB/AP = 1/3
Multiplying by 3·AP gives ...
3AB = AP
For the purpose here, we can say the lengths AB and AP are the differences ...
AB = B -A
AP = P -A
Then ...
3(B -A) = P -A
3B -3A = P -A
Adding 3A to both sides gives ...
3B = P +2A
and dividing by 3, we find B to be ...
B = (P +2A)/3
We can use this formula with the coordinates of P and A that we read from the graph to find the coordinates of B.
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Additional comment
The formula is applied separately to the x- and y-coordinates:
(Bx, By) = ((Px +2Ax)/3, (Py +2Ay)/3)
