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.