Question

Justine reflects a vector v across the y-axis. Simone reflects a vector v by rotating it 90 degrees counterclockwise about the origin. Which of the following vectors has the same image for Justine and Simone? (options are pictured)

Answer 1

A.

Explanation:

Answer 2

Answer: first choice. vector (4,4)


Justification:

1) A reflection across the y-axis keeps the y-coordinate and changes the x-coordinate to its negative.
(a,b) → (-a,b)

2) A rotation of 90° counterclockwise changes the coordinates in this way:
(a, b) → (-b, a)


3) Let's apply both transformations to the set of choices to determine which is the right choice:


Vector reflection over the y-axis rotation 90°
(x,y) (-x,y) (-y,x)

(4,4) (-4,4) (-4,4) ⇒ equals
(1,-1) (-1,-1) (1, 1) ⇒ not equals
(4,3) (-4,3) (-3, 4) ⇒ not equals
(-3,3) (3,3) (-3,-3) ⇒ not equals