Which of the following sequences of transformation takes points j(9,1) to j'(-3,7)? a) r0eflection across x-axis and translated (x, y) ( x-2, y-2). b) translated (x, y) ( x-2, y+2) and rotated 270 degrees counterclockwise about the origin. c) rotated 90 degrees counterclockwise about the origin and reflected across the x axis. or d) translated (x, y) (x-2, y+2) and rotated 90 degrees counterclockwise about the origin.

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).

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

Then translated,

Therefore option A is incorrect.

Option B:

Translated,

Then rotated 270 degrees counterclockwise about the origin.

Therefore option B is incorrect.

Option C:

Rotated 90 degrees counterclockwise about the origin

Then reflected across the x axis.

Therefore option C is incorrect.

Option D:

Translated,

Then rotated 90 degrees counterclockwise about the origin.

Therefore option D is correct.

x=half

step-by-step explanation: