4. Compositions of Isometries
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First perform the translation and then the reflection.
Let's first identify the coordinates of â–ł PNB.
To complete a glide reflection, we first perform the translation and then the reflection.
(x,y) → (x +2,y) Let's do this for the three vertices.
(x,y) | (x +2,y) | (x',y') |
---|---|---|
P(2, 2) | ( 2 +2, 2) | P'(4, 2) |
N(3,-1) | ( 3 +2,-1) | N'(5,-1) |
B(- 1,- 2) | (-1 +2,- 2) | B'(1,-2) |
With these points, we are able to draw the transformed image as â–ł P'N'B'.
To complete the reflection, we have to reflect all the vertices of â–ł P'N'B' on the opposite side of the line y=3. The distance from the vertices to the line y=3 must remain the same. We will call the reflected image â–ł P''N''B''.
The final glide reflection is the combination of the translation and the reflection.