The point R in the xy-plane with coordinates (-8,3) is reflected over the line II, given the point R' with coordinates

[BTGmoderatorLU]

Source: Magoosh

The point R in the xy-plane with coordinates (-8, 3) is reflected over the line II, giving the point R' with coordinates (-3, 8). What is the equation of the line II?

A. x = 0
B. y = 0
C. y = x
D. y = -x
E. y = -3

The OA is D

[Scott@TargetTestPrep]

Source: Magoosh

The point R in the xy-plane with coordinates (-8, 3) is reflected over the line II, giving the point R' with coordinates (-3, 8). What is the equation of the line II?

A. x = 0
B. y = 0
C. y = x
D. y = -x
E. y = -3

The OA is D

Solution:

Recall that if a point is reflected over the line y = x, the image point will have the coordinates switched. Here, we see that not only have the coordinates of R’ been switched, but they are also negated. In that case, the line of reflection must be y = -x.

Answer: D

[swerve]

Source: Magoosh

The point R in the xy-plane with coordinates (-8, 3) is reflected over the line II, giving the point R' with coordinates (-3, 8). What is the equation of the line II?

A. x = 0
B. y = 0
C. y = x
D. y = -x
E. y = -3

The OA is D

The reflection of \((x, y)\) across line \(x=0\) is \((-x, y)\)
The reflection of \((x, y)\) across line \(y=0\) is \((x, -y)\)
The reflection of \((x, y)\) across line \(y=x\) is \((y, x)\)
The reflection of \((x, y)\) across line \(y=-x\) is \((-y, -x)\)
The reflection of \((x, y)\) across line \(y=-3\) is \((x, -6-y)\)

Therefore, D