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Consider the infinite line, $L$ in $2D$ consisting of all points $p$ such that $p.[0.3511 0.9263]= 6$. Find the point on the line closest to $(10, 20)$. Find the point on the line closest to $(4, 3)$. Find the distance from the line to both of these points.

Hi, I was reading the book $3D$ Maths Primer for Graphics and Game Development. The book mention about $2$ formulas but I don't know how to apply them.

$\text{Signed distance} = d-q.n$

$q' = q + (d-q.n)n$

for any point $q$, the point $q'$ that is the closest point on $L$ to $q$.

This is what I have tried,

Since the lines are parallel then the normal are the same so

$q' = q + (6 - q(0.3511 0.9263))(0.3511 0.9263)$

I'm stuck here.

  • 1
    Seen [this](http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html)?2011-11-20
  • 0
    Hi, I'm trying to link the given formula in solving this question but i can't solve it.2011-11-20
  • 0
    Can you please use math formatting for the formulas. And accept an answer as a solution soon.2012-04-19

2 Answers 2