Scaling a shape changes lengths and areas at different rates.
WHAT HAPPENS IF…What happens to area when k=2?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideaDk(v)=kv,L′=∣k∣L,A′=k2A
Both a base and its perpendicular height scale in magnitude by |k|, so their product scales by k². Negative k also applies a half-turn about the center. At k=0 the shape degenerates and ordinary angle comparisons no longer apply.
A detail that matters
Doubling every length does not merely double area.