anonymous
  • anonymous
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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
......convert from parametric to regular than show they are the same...
anonymous
  • anonymous
so L1= P1(3,1) P2 (2,3) and L2= P1(-1,9) P2( 2,3)
anonymous
  • anonymous
why are the P1's not the same

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amistre64
  • 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?
amistre64
  • 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
asnaseer
  • 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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