anonymous 4 years ago show that the lines L1 and L2 are the same. L1 is x=3-t and y=1+2t L2 is x=-1+3t and y= 9-6t

1. anonymous

......convert from parametric to regular than show they are the same...

2. anonymous

so L1= P1(3,1) P2 (2,3) and L2= P1(-1,9) P2( 2,3)

3. anonymous

why are the P1's not the same

4. amistre64

$L1={{3}\choose{1}}+t{{-1}\choose{2}}$ $L2={{-1}\choose{9}}+t{{3}\choose{-6}}$ $L2=-\frac{1}{3}{{3}\choose{27}}-3t{{-1}\choose{2}}$ you sure you aint got a typo in there?

5. amistre64

if they are the same line we can scale L2 or L1 to get the other one, but as is there seems to be an issue

6. asnaseer

for L1 we have:\begin{align} x&=3-t\implies t=3-x\\ y&=1+2t=1+2(3-x)=1+6-2x=7-2x \end{align}for L2 we have:\begin{align} x&=-1+3t\implies t=\frac{x+1}{3}\\ y&=9-6t=9-6(\frac{x+1}{3})=9-2(x+1)=9-2x-2=7-2x \end{align}therefore L1 and L2 are the same line.

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