Let a new straight line L = 2X- 1 generated from the straight line Y, then the L equation is Y=2X+b,

Let the L and Y axes intersect at point F, take direction A as the vertical line, and the vertical foot as E, then AE= 1. In the AEF of RT triangle, ∠EAF is equal to the angle between straight line Y=2x- 1 and the positive direction of X axis, that is, the tangent of ∠EAF is equal to straight line Y=2x- 1.

The coordinates of the intersection of b and c are obtained from the l equation and the curve y = 2/x.

Calculate BC value according to the distance formula between two points.

Then the area of the triangle ABC = 1 times BC times AE.