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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)

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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
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SiddharthR
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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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