Can u please help me in finding the image of a point wrt line in 2d space using a intuitive method?
- Thread starter Abhi1
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To derive that I would first draw a sketch of the line (y = mx + c) and the point. Next I would drop a perpendicular to the line from the given point and continue...
Please share your work/thoughts for further help.
Otis
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Hi Abhi1. Another approach is to set up a system of two equations, using the Midpoint Formula (to write the first equation) and the slope relationship relating perpendicular lines (to write the second equation). Do those three things seem familiar?
EG from mathstack:
Mirror line: 2y = x + 1
Given point: (3, -3)
Image point: (a, b)
The line connecting the points is perpendicular to the given line. The lines' intersection is the midpoint between the two points. Substituting midpoint coordinates into the given line yields:
2(b - 3)/2 = (a + 3)/2 + 1
The product of the perpendicular-line slopes is -1, from which we get:
(-3 - b)/(3 - a) = -2
Solve the system of two equations, to find (a,b) = (-1,5)
?
[imath]\;[/imath]
EG from mathstack:
Mirror line: 2y = x + 1
Given point: (3, -3)
Image point: (a, b)
The line connecting the points is perpendicular to the given line. The lines' intersection is the midpoint between the two points. Substituting midpoint coordinates into the given line yields:
2(b - 3)/2 = (a + 3)/2 + 1
The product of the perpendicular-line slopes is -1, from which we get:
(-3 - b)/(3 - a) = -2
Solve the system of two equations, to find (a,b) = (-1,5)
?
[imath]\;[/imath]
Thx a lot man!! I used to do this but forgot