Line/P,Parlel,L
Parallel Line Through Point
Creates a line parallel to an existing line passing through a specific point. No selector needed.
What It Does
The Line/P,Parlel,L operator creates a line parallel to an existing line that passes through a specific point. A point and a direction uniquely determine a line — no selector is required.
Syntax
Line/P1, Parlel, L1
Quick Input
P: [point reference]
L: [reference line to be parallel to]
Direction Selector
No direction selector is required. The result is uniquely determined by the input geometry.
Worked Examples
Setup:
L0: slope=3, equation y=3x-10
P0 = (20, 50)
Line/P0, Parlel, L0
→ L1: through (20,50), slope=3
equation: y-50 = 3(x-20) → y=3x-10
Setup:
L1: horizontal at Y=30
P1 = (40, 70)
Line/P1, Parlel, L1
→ L2: horizontal at Y=70 (same slope as L1)
Analytic Rule
Direction = same as reference line L.
Line passes through point P.
Unique solution — no selector needed.
For reference line slope m:
New line: y - py = m * (x - px)
Result: Exact analytic parallel line.
FAQ
When would I use this instead of Line/Parlel,L,D?
Use Line/P,Parlel,L when you know the point the line must pass through. Use Line/Parlel,L,D when you know the perpendicular distance from the reference line.
Is the result always parallel to the reference line?
Yes. The new line has exactly the same slope as the reference line. The only difference is the Y-intercept, determined by the point P.