Exercise 20 Page 460

Let's consider the given trapezoid.

Translations are done by adding or subtracting values from the $x\text{-}$coordinate if the figure is being moved left or right, and from the $y\text{-}$coordinate if the figure is being moved up or down. We want to draw the image of our figure after a translation $3$ $\text{units}$ $\text{right}$ and $7$ $\text{units}$ $\text{down}.$ Therefore, we will $\text{add}$ $3$ to the $x\text{-}$coordinate and $\text{subtract}$ $7$ from the $y\text{-}$coordinate of each vertex.

Vertices of $ABCD$	$(x+3,y-7)$	Vertices of $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$
$A(\text{-}5,2)$	$(\text{-}5+3,2-7)$	$A^{\prime }(\text{-}2,\text{-}5)$
$B(\text{-}1,2)$	$(\text{-}1+3,2-7)$	$B^{\prime }(2,\text{-}5)$
$C(\text{-}2,4)$	$(\text{-}2+3,4-7)$	$C^{\prime }(1,\text{-}3)$
$D(\text{-}3,4)$	$(\text{-}3+3,4-7)$	$D^{\prime }(0,\text{-}3)$

Let's do the translation! As we can see, the coordinates of $C^{\prime }$ are $(1,\text{-}3).$