Justine reflects a vector v across the y-axis. simonne reflects a vector v by rotating it 90° counterclockwise about the origin. which of the following vectors has the same image for justin and simonne?

Since you have not included the choices, I will explain you how do you find the image of those transformations and give some examples

1) Justine reflects a vector v across the y-axis.
 

A reflection accross the y-axis changes the x-coordinate to negative x and keeps the y-coordinate: x,y→ - x,y


So, let v = (v₁, v₂) be the vector reflected by Justine, then its image after reflecting accross the y-axis is (-v₁, v₂)


2) Simonne reflects a vector v by rotating it 90° counterclockwise about the origin

Rotation of 90° counterclockwise changes the coordinates in this way x,y → (-y, x).

So, let u = (u₁, u₂) be the vector rotated by Simonne, then its image is (-u₂, u₁)

3) Then, by comparing the two images the condition is -v₁ = -u₂ and v₂ = u₁.

That is the same that saying the vectors have the form (a,b) and (b,a).

Now you can see some pairs of vectors that meet that:

(1,2) and (2,1)
(3,7) and (7,3)
( - 8, 5) and ( 5, -8)
( - 10, - 6) and ( - 6, - 10)
(4, - 9) and ( - 9, 4)

That is, just verify each pair and those that meet the contition x₁ = y₂ and y1 = x₂ are solutions.

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