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)

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

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