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

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BTGmoderatorLU: Moderator; Posts: 2558; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Nov 13, 2020 4:45 am

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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

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Source: Beat The GMAT — Problem Solving | Fri Nov 13, 2020 4:45 am

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

by Scott@TargetTestPrep » Mon Nov 16, 2020 12:27 pm

BTGmoderatorLU wrote: ↑
Fri Nov 13, 2020 4:45 am
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

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swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Tue Nov 17, 2020 11:12 am

BTGmoderatorLU wrote: ↑
Fri Nov 13, 2020 4:45 am
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

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