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: Determine the horizontal translation

Let's take a point, say \(A(-1,-2)\) and its image \(A'(-4,0)\).
The horizontal change: \(x\) - coordinate of \(A\) is \(-1\), \(x\) - coordinate of \(A'\) is \(-4\).
The formula for horizontal translation is \(x'=x + a\), so \(-4=-1 + a\), then \(a=- 3\).

Step2: Determine the vertical translation

The vertical change: \(y\) - coordinate of \(A\) is \(-2\), \(y\) - coordinate of \(A'\) is \(0\).
The formula for vertical translation is \(y'=y + b\), so \(0=-2 + b\), then \(b = 2\).

The rule for translation \(T_{a,b}(x,y)=(x + a,y + b)\), substituting \(a=-3\) and \(b = 2\) gives \(T_{-3,2}(x,y)\)

Answer:

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