Question

The triangle below is reflected over the line x = 4.

Which transformation(s) would produce the same image?
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A Reflecting over the x-axis and then translating to the right 4 units
B. Reflecting over the y-axis and then translating to the right 4 units
C Reflecting over the y-axis and then translating to the right 8 units
D Reflecting over the x-axis and then translating to the right 8 units

Answer 1

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Answer:

C. Reflecting over the y-axis and then translating to the right 8 units

Explanation:

Reflection over the line x=4 gives you the transformation ...

(x, y) ⇒ (2·4 -x, y) = (-x +8, y)

This is precisely the same transformation you get by reflection over the y-axis:

(x, y) ⇒ (-x, y)

followed by translation to the right 8 units:

(-x, y) ⇒ (-x +8, y)

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Reflection over x=4 is the same as reflection over y and translation right 8.