Question

the blue figure is a translation image of the black figure. write a rule to describe the translation. the translation rule is t (x,y).

Explanation:

Step1: Observe horizontal shift

Count the number of units the black - triangle moves horizontally to get to the blue - triangle. The black - triangle moves 2 units to the right. In a translation rule for the x - coordinate, moving to the right means adding a positive number. So the change in the x - coordinate is \(x+2\).

Step2: Observe vertical shift

Count the number of units the black - triangle moves vertically to get to the blue - triangle. The black - triangle moves 3 units up. In a translation rule for the y - coordinate, moving up means adding a positive number. So the change in the y - coordinate is \(y + 3\).

Answer:

\(T_{(2,3)}(x,y)=(x + 2,y+3)\)