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The point R in the xy-plane with coordinates (–8, 3) is reflected over
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shridhar786
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The point R in the xy-plane with coordinates (–8, 3) is reflected over [#permalink] New post  28 Sep 2019, 11:03
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The point R in the xy-plane with coordinates (–8, 3) is reflected over the line ll, giving the point R’ with coordinates (–3, 8). What is the equation of the line ll?

(A) x = 0

(B) y = 0

(C) y = x

(D) y = – x

(E) y = –3
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satya2029
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Re: The point R in the xy-plane with coordinates (–8, 3) is reflected over [#permalink] New post  29 Sep 2019, 21:07
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shridhar786 wrote:
The point R in the xy-plane with coordinates (–8, 3) is reflected over the line ll, giving the point R’ with coordinates (–3, 8). What is the equation of the line ll?

(A) x = 0

(B) y = 0

(C) y = x

(D) y = – x

(E) y = –3


Since it is about reflection, mid point of line joining both the given points will lie on the line II.
Mid point is (-8-3)/2, (3+8)/2=(-11/2, 11/2)
For positive value of Y, X is negative( Magnitude is also same for both the values)
Hence Y= -X
D:)
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nick1816
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Re: The point R in the xy-plane with coordinates (–8, 3) is reflected over [#permalink] New post  29 Sep 2019, 21:22
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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)

D

shridhar786 wrote:
The point R in the xy-plane with coordinates (–8, 3) is reflected over the line ll, giving the point R’ with coordinates (–3, 8). What is the equation of the line ll?

(A) x = 0

(B) y = 0

(C) y = x

(D) y = – x

(E) y = –3
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Re: The point R in the xy-plane with coordinates (–8, 3) is reflected over [#permalink] New post  22 May 2020, 16:04
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nick1816 wrote:
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)

D

shridhar786 wrote:
The point R in the xy-plane with coordinates (–8, 3) is reflected over the line ll, giving the point R’ with coordinates (–3, 8). What is the equation of the line ll?

(A) x = 0

(B) y = 0

(C) y = x

(D) y = – x

(E) y = –3




I don't understand the following one "The reflection of (x, y) across line y=-3 is (x, -6-y)" How do you get this ?
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nick1816
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Re: The point R in the xy-plane with coordinates (–8, 3) is reflected over [#permalink] New post  23 May 2020, 15:04
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Distance of (x,y) from x-axis = y

Distance of y= -3 from x-axis = 3

Distance of (x,y) from y= -3 is equal to y+3

Since (x,y') is the reflection of the (x,y) wrt line y=-3, distance of (x,y') from y=-3 is equal to y+3.

Distance of (x,y') from x-axis = |y'| = y+3+y+3-y = 6+y

Since y'< 0, y' = -6-y
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ScottTargetTestPrep
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Re: The point R in the xy-plane with coordinates (–8, 3) is reflected over [#permalink] New post  28 Nov 2020, 12:08
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shridhar786 wrote:
The point R in the xy-plane with coordinates (–8, 3) is reflected over the line ll, giving the point R’ with coordinates (–3, 8). What is the equation of the line ll?

(A) x = 0

(B) y = 0

(C) y = x

(D) y = – x

(E) y = –3

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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Re: The point R in the xy-plane with coordinates (8, 3) is reflected over [#permalink] New post  16 Mar 2022, 08:05
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Re: The point R in the xy-plane with coordinates (8, 3) is reflected over [#permalink]
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