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February 11th, 2019, 02:49 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3  Projecting points on a line  2D
a = (1, 0) b = (1, 1) c = (0, 1) L: x + y = 4/3 $\displaystyle Proj_{L}(a) = ? \\ Proj_{L}(b) = ? \\ Proj_{L}(c) = ? \\ $ 1. How do I express x + y = 4/3 in matrix form for projection matrix multiplication? 2. Is it possible to calculate the projection{a,b,c} on L with matrix multiplication? 
February 11th, 2019, 04:42 PM  #2 
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 
Plain Old Algebra $\displaystyle A = (0, 1) \\ L: x + y = 4/3 \\ \perp(L) : x = y \\ Point~A~lies~on~ \perp(L) : ax + b = c, (0) + b = 1, b = 1 \\ L_{1}: x + 1 = y \\ The~intersection~point~between~L~and~L_{1}: x + 1 = 4/3  x \\ The~intersection~point: (1/6, 7/6) $ $\displaystyle B = (1, 1) \\ Point~B~lies~on ~\perp(L): ax + b = c, (1) + b = 1, b = 0 \\ L_{2}: x = y \\ The~intersection~point~between~L~and~L_{2}: x = 4/3  x \\ The~intersection~point: (2/3, 2/3) $ $\displaystyle C = (1, 0) \\ Point~C~lies~on ~\perp(L): ax + b = c, (1) + b = 1, b = 1 \\ L_{3}: x  1 = y \\ The~intersection~point~between~L~and~L_{3}: x 1 = 4/3  x \\ The~intersection~point: (7/6, 1/6) $ Case closed... Last edited by zollen; February 11th, 2019 at 04:50 PM. 
February 11th, 2019, 04:52 PM  #3 
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 
I was hoping I could have used projection matrix to solve this problem...


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line, points, projecting 
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