The series of transformations that maps EFGH onto its image is a reflection across the y-axis, followed by a translation 4 units to the left, and finally a dilation by a factor of 3.
The series of transformations involving a reflection, translation, and dilation that maps EFGH onto its image is:
1. Reflection across the y-axis
2. Translation 4 units to the left
3. Dilation by a factor of 3
**Calculations:**
Reflection across the y-axis:
E(4, 3) -> E'(-4, 3)
F(4, 2) -> F'(-4, 2)
G(4, -3) -> G'(-4, -3)
H(4, -7) -> H'(-4, -7)
Translation 4 units to the left:
E'(-4, 3) -> E''(-8, 3)
F'(-4, 2) -> F''(-8, 2)
G'(-4, -3) -> G''(-8, -3)
H'(-4, -7) -> H''(-8, -7)
Dilation by a factor of 3:
E''(-8, 3) -> E'''(-24, 9)
F''(-8, 2) -> F'''(-24, 6)
G''(-8, -3) -> G'''(-24, -9)
H''(-8, -7) -> H'''(-24, -21)
Therefore., series of transformations that maps EFGH onto its image is a reflection across the y-axis, followed by a translation 4 units to the left, and finally a dilation by a factor of 3.