Question

The coordinates of the end of points of a segment are p1(2,4) and p2(8,-4). Find the point p(x,y) such that it splits the segment in the ratio (r=p2p/pp1) equal to -2. I have tried many thing, please help

Answer 1

I don't get the ratio thing. How would you evaluate p_2*p? They're vectors, not numbers.

Answer 2

The distance from p2 to p divided by the distance p to p1 equals -2. Does it make sense now?

Answer 3

that does make more sense.

Answer 4

|p_2-p|=-2|p_1-p|
\[\sqrt{(8-x)^{2}+(-4-y)^{2}}=-2\sqrt{(2-x)^{2}+(4-y)^{2}}\]

Answer 5

\[(8-x)^{2}+(-4-y)^{2}=-2(2-x)^{2}+(4-y)^{2}\]

Answer 6

\[x^2-16x+80+8y+y^2=-2x^2+8x-8-32+16y-2y^2\]

Answer 7

I imagine this is going somewhere...

Answer 8

This is the farther i got

Answer 9

\[-x^2-24x+120=-3y^2+8y\]

Answer 10

\[x^2+24x+120=3y^2-8y\]

Answer 11

That's one relation for x and y, the other one is that's on the line.

Answer 12

y=8/6x+c

Answer 13

There is a specific formula for these questions

Answer 14

I know that the answer is a real number

Answer 15

2=32/6+c
c=-20/6

Answer 16

It'd be a miracle if I didn't make any computation mistakes yet.

Answer 17

6y=8x-20

Answer 18

Now you can put this into the quadratic equation to get a quadratic equations of one variable. Solve that for that variable and then use 6y=8x-20 again to find the other variable.

Answer 19

Are you still following this?

Answer 20

yes

Answer 21

can we talk through skype? for a better explanation. I got lost midway

Answer 22

I don't have skype...

Answer 23

ok let me see where I got lost. Trying to figure out the last part

Answer 24

Sure, take your time.

Answer 25

what is relation for x and y, and how do I find it

Answer 26

Can we use twidlla in the following link?
http://www.twiddla.com/625822

Answer 27

ok

Answer 28

I'm at the link.