Question

Which glide reflection describes the mapping Triangle ABC to DEF

Answer 1

`(x,y)\rightarrow (x, y-7)\text{ and reflected across x = 4}`

Explanation:

∵ The rule of reflection across x = 4,

`(x,y)\rightarrow (8-x,y)`

Rule of reflection across y = 4

`(x,y)\rightarrow (x, 8-y)`

Rule of reflection across x = 0

`(x,y)\rightarrow (-x,y)`

Thus,
`(x,y)\rightarrow (x, y-7)\text{ and reflected across x = 4}`

`\implies (x,y)\rightarrow (x,y-7)\rightarrow (8-x, y-7)`

`(x,y)\rightarrow (x-3, y)\text{ and reflected across x = 4}`

`\implies (x,y)\rightarrow (x-3,y)\rightarrow (11-x, y)`

`(x,y)\rightarrow (x-3, y)\text{ and reflected across y = 4}`

`\implies (x,y)\rightarrow (x-3,y)\rightarrow (x-3, 8-y)`

`(x,y)\rightarrow (x, y-7)\text{ and reflected across x = 0}`

`\implies (x,y)\rightarrow (x,y-7)\rightarrow (-x, y-7)`

Here, the coordinates of triangle ABC are,

A ≡ (3, 3), B≡(7,6), C≡(7,2)

And, the coordinates of transformed triangle,

D ≡ (5,-4) E≡(1,-1), F≡(1,-5)

Therefore, by the above explanation,

The glide reflection that shows the mapping
`\triangle ABC\rightarrow \triangle D EF` is,

`(x,y)\rightarrow (x, y-7)\text{ and reflected across x = 4}`

Answer 2

The correct option is A.

Explanation:

The correct option is A.

If u notice the second transformation it would shift triangle ABC 3 units to the left and reflect it across x = 4 so this will not map ABC into DEF.

If u notice first transformation it will shift triangle ABC 7 units down and reflect it across x=4 so this will map ABC into DEF.

Thus option A is correct....