Suppose a line goes through the points A = ( x 1 , y 1...
Suppose a line goes through the points and . One can easily check (as I did today while doodling) that
where is the y-coordinate of the -intercept. This can be written more suggestively as
The presence of det(A,B) suggests a geometrical interpretation, but I couldn't think of one. This reminds me of Cramer's Rule, but I couldn't make that connection explicit either.