Analytical Geometry (Division of line segments)

[at94official]

1. Here is the Problem:

A line passes through A(2,3) and B(5,7).
Find:

(a) the coordinates of the point P on AB
extended through B to P so that P is twice as far from A as from B;
(b) the coordinates if P is on AB extended through A so that P is twice as far from B as from A.

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Homework Equations

:[/B]
To get the coordinates P, here is the equation i used:
X_P=X₁+R(X₂-X₁)

R is the Ratio of AP/AB

I'll do the same for Y_p

The Attempt at a Solution

:
[/B]
So this is my attempt to solve the (a) P Coordinates.

AP = 2BP

R=AP/AB=2/1=2

X = X₁+R(X₂-X₁)
X = 2+2(5-2)
X = 2+2(3)
X = 2+6
X = 8

For Y:

Y = 3+2(7-3)
Y = 3+2(4)
Y = 3+8
Y = 11

∴ (a)P (8,11)As i attempt to graph it. It seems like it is too much based on the problem. What did I miss?

 

[LCKurtz]

Your solution looks fine.