Question

Which of the following sequence of transformations takes point J(9, 1) to J’(-3, 7)?

reflected across x-axis and translated (x, y) → (x - 2, y - 2)
translated (x, y) → (x - 2, y + 2) and rotated 270° counterclockwise about the origin
rotated 90° counterclockwise about the origin and reflected across x-axis
translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

Answer 1

translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

Explanation:

The image point is in the 3rd quadrant, and the pre-image point is in the first quadrant. This means there has been any of ...

• reflection across the y-axis
• translation
• rotation 90° CCW

The only answer choice involving the appropriate rotation is ...

translated (x, y) → (x - 2, y + 2) and rotated 90° counterclockwise about the origin

__

Checking this, we have

(x, y) ⇒ (x -2, y +2) . . . . translation left 2, up 2

(x -2, y +2) ⇒ (-y -2, x -2) . . . . followed by 90° CCW rotation

J(9, 1) ⇒ J'(-3, 7) . . . . . consistent with the given image point