How do you determine a minimum area triangle, given 2 sides and a point on the third side?

Question

Two lines with equations: y = 2 – (1/2)x and (x-1) = 2 (y-1) respectively are graphed on a Cartesian plane. A line is drawn through the point (2, -1) which intersects the two previous lines to give a triangle of minimum area. What is that area?

Answer 1

The two given lines intersect.

A straight line through (2,-1) will form several different triangles depending on the slope of the straight line.

At least for me it is unclear which triangle is to have minimum area, especially since the line through (2,-1) and the point of intersection does not form a triangle (or a triangle of 0 area if you want to think of it that way).