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) <span>Justine reflects a vector v across the y-axis. </span><span> </span><span> </span><span>A reflection accross the y-axis changes the x-coordinate to negative x and keeps the y-coordinate: x,y→ - x,y </span><span> </span><span> </span><span>So, let v = (v₁, v₂) be the vector reflected by Justine, then its image after reflecting accross the y-axis is (-v₁, v₂) </span>
2)<span> Simonne reflects a vector v by rotating it 90° counterclockwise about the origin</span>
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.
