SOLUTION: The segment AB is one third of the entire length of segment AD. If A(3,-2) and B(0,2), then where is the terminal point D located?

Question 1074065: The segment AB is one third of the entire length of segment AD. If A(3,-2) and B(0,2), then where is the terminal point D located?
Found 3 solutions by mananth, greenestamps, ikleyn:
Answer by mananth(16949)   (Show Source): You can put this solution on YOUR website!
We have to use section formula for internal division
if we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:
P(x, y) = (mx2+nx1)/(m+n), (my2+ny1)/(m+n)
.
A= (x2,y2)~(3,-2)
B= (x,y) ~(0,2)
m=1 , n=2
0= (1(x)+(2)(3))/3
x=-6
2= ((1)(y)+(2)(-2))/3
6= y-4
y=10
x(-6,10)

Answer by greenestamps(13250)   (Show Source): You can put this solution on YOUR website!

Of course, we don't HAVE to use the formula shown by the other tutor. If you want to solve the problem using formal mathematics, there are alternative forms of the formula that make it easier to understand.

But solving the problem informally using common sense is MUCH easier.

B is one-third of the distance from A to D.

In the x direction, from A to B is a change of -3, so from A to D the change in the x direction is 3(-3) = -9. So the x coordinate of D is 3+(-9) = -6.

In the y direction, from A to B is a change of +4, so from A to D the change in the y direction is 3(+4) = +12. So the y coordinate of D is (-2)+12 = 10.

ANSWER: D(-6,10)

Answer by ikleyn(53369)   (Show Source): You can put this solution on YOUR website!
.
The segment AB is one third of the entire length of segment AD.
If A(3,-2) and B(0,2), then where is the terminal point D located?
~~~~~~~~~~~~~~~~~~~~~

By the way, segment AD may have an OPPOSIITE direction comparing with AB,

or any other direction on the plane, different from that of AB, so this problem,
as it is worded in the post, is HEAVILY DEFECTIVE.

From the written post, it remains unclear how the point B does relate to the segment AD.

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