The quadrants of the standard \((x,y)\) coordinate plane are shown below. The vertices of \(\triangle{ABC}\) are \(A(-3,3)\), \(B(-3,1)\), and \(C(-1,1)\). The triangle is translated by \(x'=x+5\) and \(y'=y-2\). The image of \((x,y)\) on \(\triangle{ABC}\) is \((x',y')\) on \(\triangle{A'B'C'}\). The vertices of \(\triangle{A'B'C'}\) lie in which quadrant(s)?

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Translate each point according to the rules.

$$ A(-3,3) \rarr A'(2,1) $$ $$ B(-3,1) \rarr B'(2,-1) $$ $$ C(-1,1) \rarr C'(4,-1) $$

The image lies in quadrants I and IV.