Question

which rule represents the translations below? (x,y)→(x - 4,y + 4) (x,y)→(x - 4,y - 4) (x,y)→(x + 4,y - 4) (x,y)→(x + 4,y + 4)

Explanation:

Step1: Analyze horizontal shift

Observe the x - coordinates of corresponding points. The figure moves 4 units to the right. In a coordinate transformation, moving 4 units to the right means adding 4 to the x - coordinate, so the new x - coordinate is \(x+4\).

Step2: Analyze vertical shift

Observe the y - coordinates of corresponding points. The figure moves 4 units up. In a coordinate transformation, moving 4 units up means adding 4 to the y - coordinate, so the new y - coordinate is \(y + 4\). The transformation rule is \((x,y)\to(x + 4,y+4)\).

Answer:

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