Question

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A series of transformations maps EFGH onto its image.

Determine the series of transformations involving a reflection, translation, and dilation that maps EFGH onto its image. In your final answer, include all of your calculations.

Answer 1

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.