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(52790)  (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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