# Homework Help: Proving that this equation goes through the points

1. Mar 25, 2009

### unknown101

1. The problem statement, all variables and given/known data
Use a vector solution to show that a scalar equation for the line through the points P1(x1,y1) and P2(x2,y2) is y-y1/x-x2=y2-y1/x2-x1

2. Relevant equations
Find a vector which is normal to the line and then use the dot product of this vector and P1P

3. The attempt at a solution
I tried using numbers but I got lost. I don't what exactly this question is asking. Would I have to find the slope and then come up with a solution from that?

2. Mar 25, 2009

### tiny-tim

Hi unknown101!

Hint: call a point on the line P.

What do you know about the vectors PP1 and P1P2 ?

3. Mar 26, 2009

### unknown101

OK so I call a point P. I don't know what you mean about those two vectors. Would I have to find the m which is the slop and then n which is the normal point. Looking at my notes none of this makes sense

4. Mar 26, 2009

### tiny-tim

vector maths

ah … doesn't look as if your teacher has introduced you to the joys of vector maths, as opposed to coordinate maths.

Vector maths tries to avoid using coordinates …

for example, (a + b)2 = a2 + 2a.b + b2 is proved by simple algebra, and is a lot easier than the coordinate proof!

In vector maths, you can only really use three combinations …

a.b, axb, and ka (where k is a constant) …

which one(s) do you think would help in proving that PP1 is parallel to P1P2 ?

5. Mar 26, 2009

### unknown101

Would I use a.b to prove that is it parallel?

6. Mar 26, 2009

### tiny-tim

It's easier to use a = kb

7. Mar 26, 2009

### unknown101

So if I use a=kb will I have to find the constant. Looking at the equation I'm trying to prove, do I have to to find out what y and x( the x and y without the number)?

8. Mar 27, 2009

### tiny-tim

Hint: write a = kb in coordinates, and see if you can eliminate k.

9. Mar 27, 2009

### unknown101

I wrote a=kb in coordinates. I don't if I did it correctly.
x1y1=k(x2y2)
x1k1/x2y2=k

Is that all i need to do?

10. Mar 27, 2009

### tiny-tim

you're making it look like one equation …

it's (x1 , y1) = k(x2 , y2), which is two equations …

so write them out and eliminate k

11. Mar 27, 2009

### unknown101

So I did that I got (x1, y1)/x2, y2)=k

12. Mar 27, 2009

### unknown101

So this is the final answer?

13. Mar 27, 2009

### tiny-tim

uhhh?

that doesn't even make sense …

you can't divide a vector by another vector

write two equations

14. Mar 27, 2009

### unknown101

You said I should write out 2 equations:
(x1,y1)=k(x2,y2)
x1,y1=kx2,ky2
Is that right?

15. Mar 27, 2009

### tiny-tim

Yes … but it would be clearer if you wrote it explicitly as two equations …

anyway, now eliminate k

16. Mar 27, 2009

### unknown101

By writing as two equations do you mean as in...
1.(x1,y1)
2.(kx2,ky2)

Eliminate k. The only way I can think for eliminating k is
kx2,ky2=0
kx2,ky2/k=o/k
x2,y2=0

I don't know if I'm doing this right.

17. Mar 27, 2009

### tiny-tim

They aren't equations …

?? this doesn't make any sense at all

write (x1 , y1) = k(x2 , y2) as two equations …

that's two completely separate sentences, each with an = in the middle

18. Mar 27, 2009

### unknown101

Ok I kind of understand it now.
This is what I have so far
x1,y1=kx2,ky2
(x1,y1)/(k,k)=(kx2,ky2)/(k,k)
(x1,y1)/(k,k)=(x2,y2)

19. Mar 27, 2009

### unknown101

Is that right?