Question

Which glide reflection describes the mapping Triangle ABC to DEF

Answer 1

Answer:

The correct option is A.

Step-by-step 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....

Answer 2

Answer:

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

Step-by-step 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,

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