Find the image of o (0,0) after two reflections,first in l1 and then l2 . l1:x= -2, l2: y-axis

two-reflections

#1

find the image of o (0,0) after two reflections,first in l1 and then l2 . l1:x= -2, l2: y-axis

Answer:

Line x=−2 is a vertical line with first coordinate x being −2 for all the points on that line.

To reflect the point (0,0) over this line we first find the distance of the point to the line.

Distance is |−2−0|=|−2|=2.

Since the line is vertical, y− coordinate of (0,0) won’t change. Point (0,0) is on the right side of the line x=−2 so when we reflect it, it will be on the left side.

The point becomes (0−2⋅2,0)=(−4,0).

We subtracted two distances from the first coordinate and second coordinate remained the same.

Now find reflection of (−4,0) over the y−axis. Distance is |−4−0|=|−4|=4. Same reasoning as before gives us result:

(−4+2⋅4,0)=(4,0)