Respuesta :
Answer: option D) translated (x,y) (x-2, y+2) and rotated 90 degrees counterclockwise about the origin.
Justification:
1) Translation (x,y) → (x - 2, y + 2) ⇒ (9, 1) → (9 - 2, 1 + 2) = (7, 3)
2) Rotation 90° counterclokwise ⇒ (x, y) → (-y, x) ⇒ (7, 3) → (-3, 7)
So, there you have the demonstration that the translation of J (9,1) according to (x,y) → (x - 2, y + 2), followed by a rotation of 90° counterclockwise produces the image J' (-3, 7).
Answer:
The correct option is D.
Step-by-step explanation:
It is given that sequences of transformation takes points J(9,1) to J'(-3,7).
Option A:
Reflection across x-axis
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex]J(9,1)\rightarrow J_1(9,-1)[/tex]
Then translated,
[tex](x,y)\rightarrow (x-2,y-2)[/tex]
[tex]J_1(9,-1)\rightarrow J'(7,-3)\neq J'(-3,7)[/tex]
Therefore option A is incorrect.
Option B:
Translated,
[tex](x,y)\rightarrow (x-2,y+2)[/tex]
[tex]J(9,1)\rightarrow J_1(7,3)[/tex]
Then rotated 270 degrees counterclockwise about the origin.
[tex](x,y)\rightarrow (y,-x)[/tex]
[tex]J_1(7,3)\rightarrow J'(3,-7)\neq J'(-3,7)[/tex]
Therefore option B is incorrect.
Option C:
Rotated 90 degrees counterclockwise about the origin
[tex](x,y)\rightarrow (-y,x)[/tex]
[tex]J(9,1)\rightarrow J_1(-1,9)[/tex]
Then reflected across the x axis.
[tex](x,y)\rightarrow (x,-y)[/tex]
[tex]J_1(-1,9)\rightarrow J'(-1,-9)\neq J'(-3,7)[/tex]
Therefore option C is incorrect.
Option D:
Translated,
[tex](x,y)\rightarrow (x-2,y+2)[/tex]
[tex]J(9,1)\rightarrow J_1(7,3)[/tex]
Then rotated 90 degrees counterclockwise about the origin.
[tex](x,y)\rightarrow (-y,x)[/tex]
[tex]J_1(7,3)\rightarrow J'(-3,7)[/tex]
Therefore option D is correct.
