Plot Plot A(2,2) B(6,2) D(2,5) E and E(4,7) Translate the object using (x,y) -> (x+3, y+2) Reflect the translated image x-axis. Use an scale of 2cm to 2units A(2+3) -> A(5,4) -> (2+2) x-y -> (x-y) A(5-4)

The problem states the object has vertices $A(2,2)$, $B(6,2)$, $D(2,5)$, and $E(4,7)$.
The initial coordinates are:

• $A(2,2)$
• $B(6,2)$
• $D(2,5)$
• $E(4,7)$

We apply this translation rule to each vertex:

• For $A(2,2)$: $A' = (2+3, 2+2) = (5,4)$
• For $B(6,2)$: $B' = (6+3, 2+2) = (9,4)$
• For $D(2,5)$: $D' = (2+3, 5+2) = (5,7)$
• For $E(4,7)$: $E' = (4+3, 7+2) = (7,9)$ The coordinates of the translated image are $A'(5,4)$, $B'(9,4)$, $D'(5,7)$, and $E'(7,9)$.

The rule for reflection across the x-axis is $(x,y) \to (x, -y)$. We apply this rule to the translated vertices:

• For $A'(5,4)$: $A'' = (5, -4)$
• For $B'(9,4)$: $B'' = (9, -4)$
• For $D'(5,7)$: $D'' = (5, -7)$
• For $E'(7,9)$: $E'' = (7, -9)$

The final coordinates of the reflected image are $\boxed{\mathbf{A''(5, -4), B''(9, -4), D''(5, -7), E''(7, -9)}}$.
(The instruction "Use a scale of 2cm to 2 units" is for plotting, which is not performed here.)