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: Analyze horizontal translation

Let's take a point, say \(A(-5,1)\) in the red rectangle. Its corresponding point \(A'(-3, - 2)\) in the blue rectangle. The change in \(x\) - coordinate: \(-3-(-5)=2\). So, the horizontal translation is \(2\) units to the right (since the value is positive).

Step2: Analyze vertical translation

The change in \(y\) - coordinate: \(-2 - 1=-3\). So, the vertical translation is \(3\) units down (since the value is negative).
The rule for translation \(T_{a,b}(x,y)=(x + a,y + b)\), where \(a = 2\) and \(b=-3\)

Answer:

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