Question

irina wants to tile her floor using the translation shown below. which is the rule for this translation?
○ t_-3,2(x,y)
○ t_2,-3(x,y)
○ t_3,2(x,y)
○ t_-2,3(x,y)

Explanation:

Step1: Observe x - coordinate change

Pick a point, say the bottom - left vertex of the blue rectangle (let's call it the original point) with coordinates \((x,y)\) and its corresponding point in the red rectangle. If we look at the x - coordinates of corresponding points, we see that the x - coordinate of the new point is 3 units less than the x - coordinate of the original point. In a translation rule \(T_{a,b}(x,y)=(x + a,y + b)\), the change in the x - coordinate is given by \(a\). So \(a=-3\).

Step2: Observe y - coordinate change

Looking at the y - coordinates of corresponding points, the y - coordinate of the new point is 2 units more than the y - coordinate of the original point. In the translation rule \(T_{a,b}(x,y)=(x + a,y + b)\), the change in the y - coordinate is given by \(b\). So \(b = 2\).

Answer:

\(T_{-3,2}(x,y)\)