Question

1. what is the rule for the rigid motion? see example 2

Explanation:

Step1: Analyze x - coordinate change

For point A(-2, - 2) and A'(-6,2), the x - coordinate of A changes from - 2 to - 6. The change in x is $\Delta x=-6-( - 2)=-4$. The y - coordinate of A changes from - 2 to 2. The change in y is $\Delta y=2-( - 2)=4$.

Step2: Generalize the rule

For a point (x,y) in the original figure, the new point (x',y') after the rigid - motion has the rule: $x'=x - 4$ and $y'=y + 4$. In coordinate - notation, the rule for the rigid motion is $(x,y)\to(x - 4,y + 4)$.

Answer:

$(x,y)\to(x - 4,y + 4)$