The point R in the xy-plane with coordinates (–8, 3) is reflected over

Question

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

satya2029 · Accepted Answer

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:)

nick1816 · Answer

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

SiddharthR · Answer

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 ?

nick1816 · Answer

SiddharthR Untitled.png 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

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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The point R in the xy-plane with coordinates (–8, 3) is reflected over

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The point R in the xy-plane with coordinates (–8, 3) is reflected over

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