Question

Which sequence of transformations will map figure Konto figure Kí?109876432Х10-9-8--5-4-3-2-11 +2 3 4 5 6 7 8 9 1010Reflection across X = 4, 180° rotation about the origin, and a translation of (x + 8, y)Reflection across X = 4, 180° rotation about the origin, and a translation of (x - 8, y)Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y)Reflection across y = 4, 180° rotation about the origin, and a translation of (x - 8, y)

Answer 1

A

Step-by-step explanation:

To determine which sequence of transformation will map figure K onto figure K', we test each of the options using the point (6,5) in Figure K.

Option A

Reflection across x=4, 180° rotation about the origin, and a translation of (x+8,y)

`\left(6,5\right)\rightarrow(2,5)\rightarrow\left(-2,-5\right)\rightarrow(6,-5)`

Option B

Reflection across x=4, 180° rotation about the origin, and a translation of (x-8, y)

`\left(6,5\right)\rightarrow(2,5)\rightarrow\left(-2,-5\right)\rightarrow(-10,-5)`

Option C

Reflection across y=4, 180° rotation about the origin, and a translation of (x+8,y)

`\left(6,5\right)\rightarrow(6,3)\rightarrow\left(-6,-3\right)\rightarrow(2,-3)`

Option D

Reflection across y=4, 180° rotation about the origin, and a translation of (x-8,y)

`\left(6,5\right)\rightarrow(6,3)\rightarrow\left(-6,-3\right)\rightarrow(-14,-3)`

We can see that Option A is the one which maps point (6,5) to (6,-5).

Therefore, it is the sequence of transformations will map figure K onto figure K'.