Relationship Lab
Sweep the slope of the blue line and watch the parallel (teal) and perpendicular (gold) through the point update live — with the right-angle marker.
1 Relationship Lab
Drag m to tilt the blue line. The teal parallel and gold perpendicular through the marked point follow it — always keeping their relationships.
Relationships hold at every slider position.
2 What to notice
Three experiments.
1. The teal line never tilts differently
Sweep m: the parallel always matches the blue tilt exactly. Equal slopes, forever.
2. The gold line counter-tilts
When blue climbs steeply, gold falls shallowly — the product of their slopes stays −1.
3. m = 0 breaks the pattern beautifully
Drag m to 0: blue goes horizontal, the perpendicular becomes vertical — the special case, drawn live.