Question

which rule describes the translation?
$\circ t_{-3,-2}(x,y)$
$\circ t_{-3,2}(x,y)$
$\circ t_{3,-2}(x,y)$
$\circ t_{3,2}(x,y)$

Explanation:

Step1: Determine the horizontal translation

Count the number of units moved horizontally. From \(B(-1,2)\) to \(B'(2,0)\), the \(x -\)coordinate changes from \(-1\) to \(2\). The change in \(x\) is \(2-(-1)=3\), so it is a translation of \(3\) units to the right (positive \(x -\)direction).

Step2: Determine the vertical translation

Count the number of units moved vertically. From \(B(-1,2)\) to \(B'(2,0)\), the \(y -\)coordinate changes from \(2\) to \(0\). The change in \(y\) is \(0 - 2=-2\), so it is a translation of \(2\) units down (negative \(y -\)direction).

Answer:

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