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Solve for t

We can parameterize the ray from CC through PP as a function of tt:
R(t)=(1t)C+tP\qquad R(t) = (1-t)C + tP
With CC at (0,0)(0, 0) and PP at (3,2)(3, 2), R(t)R(t) intersects a line defined by the equation:
y=2x+12y = -2x + 12
If the intersection point is II and I=R(t)I = R(t^*), what is the value of tt^*?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
Created with RaphaëlCreated with Raphaël
1\small{1}2\small{2}3\small{3}4\small{4}5\small{5}6\small{6}7\small{7}8\small{8}9\small{9}-2\small{\llap{-}2}-3\small{\llap{-}3}-4\small{\llap{-}4}-5\small{\llap{-}5}-6\small{\llap{-}6}-7\small{\llap{-}7}-8\small{\llap{-}8}-9\small{\llap{-}9}1\small{1}2\small{2}3\small{3}4\small{4}5\small{5}6\small{6}7\small{7}8\small{8}9\small{9}-2\small{\llap{-}2}-3\small{\llap{-}3}-4\small{\llap{-}4}-5\small{\llap{-}5}-6\small{\llap{-}6}-7\small{\llap{-}7}-8\small{\llap{-}8}-9\small{\llap{-}9}yyxxPPCCy=2x+12y = -2x + 12II