Find the image of Z(1,1) after two reflections, first across line L1, and then across line L2. L1: x=2, L2: y-axis

After a reflection across line L1, x = 2, the afterimage is
Z' (2 + (2-1) ,1) = Z' (3, 1)
After a reflection across the line L2, y-axis, the afterimage is
Z'' (3, 0 + (0 - 1) = Z'' (3, -1)

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facundo3141592 facundo3141592 · Answer 2 · 2019-10-19T02:08:40+02:00

Answer: Hello there, our point is (1,1), where the notation is in (x,y)

We make two rotations, one across L1: X = 2 and other across L2: X = 0.

the first rotation is across X = 2

Then this rotation only affects the x therm in our pair.

The thing that we know about rotations, is that the distance between our point and the axis before and after the rotation, is the same in amplitude.

Then our pair has x = 1, and the axis is at x = 2

the distance between 1 and 2 is equal to 1.

then the next place of x is the number that has a distance of 1 unit from 2.

this is 2 + 1 = 3

the new value of x is 3.

The rotation across L2 is similar, now Y remains unaltered and only affects the value of x

The axis is now in x = 0, and the value of x in our pair is x = 3.

the distance between 0 and 3 is 3 units.

then the new value of x also is at a distance of 3 units from 0, the only other value that has a distance equal to 3 from 0, is y = -3

then the new value of x is -3.

our image is now Z(-3, 1)