Line Intersection
GeometryMediumVerify slope intersections of segments and infinite lines.
Alt+Shift+I
Segment Intersection Grid (Drag A, B, C, or D)
Determinant slope check:80
Lines Status:Intersecting
Intersection Point:(0.40, 0.80)
Lies Within Finite Segments:Yes (Segments intersect)
Time Complexity
O(1) direct equation
Space Complexity
O(1) auxiliary
Conceptual Overview
Line Intersection determines if two lines (infinite or finite segments) meet at a common coordinate, detecting parallel/coincident states.
Mathematical Formula
a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \\ x = \frac{b_2 c_1 - b_1 c_2}{a_1 b_2 - a_2 b_1}, \ y = \frac{a_1 c_2 - a_2 c_1}{a_1 b_2 - a_2 b_1}
Source: CP-Algorithms geometry reference