Concept guide
Similarity: deciding labeled triangle similarity at a specified positive scale and finding the area
In one equal-unit orthonormal plane, let A1=(0,0), A2=(4,0), A3=(0,2) and B1=(1,1), B2=(1,7), B3=(4,1), with correspondence Ai↔Bi and scale direction |BiBj|=k|AiAj|, at the specified k=3/2. Decide that they are similar at k=3/2, and from the given area Area(A)=4 find Area(B); then explain why k=2 is rejected only as a witness, why k=−3/2 is not eligible, and why opposite orientation does not change the positive scale.