# Math Help - basic geometry problem

1. ## basic geometry problem

Help!
Find the point of the line passing through A(-1,-1) and B(4,4) which is
(a) twice as far from A as from B (two cases).
(b) three times as far from B as from A (two cases).

I also need to graph it..Thanks.

2. Originally Posted by cannon
Help!
Find the point of the line passing through A(-1,-1) and B(4,4) which is
(a) twice as far from A as from B (two cases).
(b) three times as far from B as from A (two cases).

I also need to graph it..Thanks.
HI

For (1) , The point , call it Q divides the line internally in the ratio of 2:1 and externally in the ratio of 2:-1 .

Case 1 (internal) :

$Q=\left(\frac{(-1\times 1+4\times 2)}{2+1} , \frac{-1\times 1+4\times 2}{3}\right)$

Case 2: (external) : just flip the signs .

(2) Q divides the line in a ratio of 1:3 , and 1:-3 . Use the formula again .

3. I'm pretty confused with the ratios. In (a) the ratio is 2:1, shouldn't be (b) 1:3 but 3:1?