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 A. Its original x - coordinate in the blue rectangle and new x - coordinate in the red rectangle. If we assume an original point \((x,y)\) in the blue - rectangle and its corresponding point \((x',y')\) in the red rectangle. By looking at the horizontal shift, we see that the x - coordinate of a point changes as \(x'=x - 3\).

Step2: Observe y - coordinate change

Looking at the vertical shift of the same point, the y - coordinate changes as \(y'=y + 2\). In the translation notation \(T_{a,b}(x,y)=(x + a,y + b)\), here \(a=-3\) and \(b = 2\).

Answer:

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