Find the coordinates of P....?

Question

The straight line from A(-1,-5) to B(8,7) is divided by P in the ratio 1:2. Find the coordinates of P.

To me it looks like there are two solutions. Can anyone help me out? Please show your work or explain how you got your answer.

Thanks!

Answer 1

There are two possible answers, but my guess is that tradition dictates AP is 1 part, and PB is 2 parts of the whole segment.  Your teacher/questioner wants the P nearer to point A.

Since there are 9 units from A to B in the x-coordinate, you must go 3 units right -1 + 3 is -2.  Since 12 units from -5 to 7, you must go 4, thus y-coordinate is -1.  Your point P nearer to A is (-2,-1).  

The other possible answer is (5,3), but I'm pretty sure that makes your ratio 2:1, not 1:2.

Answer 2

I agree tht there should be 2 solutions depending on whether P is closer to A or to B.

AP/PB = 1/2

also AP+PB= sqrt[(8+1)^2 + (7+5)^2=81+144=225=15

if AP=w and PB=15-w then

w/(15-w) =1/2

2w=15-w

3w=15

w=5

2w=10

now find the coordinate of the point 5 from A, then 5 from B

use point A and the point (-1,y) and (x,y) to form a triangle, then apply the Pythagorean theorem.  For the other point, use point B, point (8,y) and (x,y) the distance of the hypotenuse will be 5. You could also use 10 and get the same results

Answer 3

There should be two possible solutions, since the problem does not specify whether point P is closer to A or closer to B.

The differences between A and B are

(8+1, 7+5) = (9, 12)

So P, which must be 1/3 of the length of segment AB from A or B, is one of the following:

(-1+9/3, -5+12/3) = (2, -1)

or

(8-9/3, 7-12/3) = (5, 3)