SOLUTION: Two points A(-5,1) and B(c,d) are given. If P(-3,2) divides AB into two parts in the ratio 2:1, find the value of c and d.

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Question 1174280: Two points A(-5,1) and B(c,d) are given. If P(-3,2) divides AB into two parts in the ratio 2:1, find the value of c and d.
Found 3 solutions by ewatrrr, greenestamps, ikleyn:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi

Two points A(-5,1) and B(c,d) are given. 
If P(-3,2) divides AB into two parts in the ratio 2:1, 
find the value of c and d.

A(-5,1) and 
P(-3,2)        ratio '2' : 1    P is over 2 up 1
B (-2, 2.5)    ratio 2 : '1'    B is over 1 up 1/2
   c  = -2  and d = 2.5




Wish You the Best in your Studies.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


On the segment AB, and on both the horizontal (x) and vertical (y) components of that segment, P divides AB in the ratio 2:1. In other words, from P to B is half as far as from A to P.

x coordinate of B...
From A to P is from -5 to -3, a change of +2, so the change from P to B is +1; c = -3+1 = -2.

y coordinate of B...
From A to P is from 1 to 2, a change of +1, so the change from P to B is +1/2 or 0.5; d = 2+0.5 = 2.5.

ANSWER: (c,d) = (-2,2.5)
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

As the problem is stated,  the point  P  on  AB  is not defined by a  UNIQUE  way.


Because it admits   AP : PB = 2   (it is what the author keeps in his mind)

and   AP : BP =   (which is out of the author's mind, but still how the problem can be interpreted).

So, as the problem is presented, IT IS NOT a WAY to present a Math problem.
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