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,y -3) Let's do this for the three vertices.
(x,y) | (x,y -3) | (x',y') |
---|---|---|
P(2, 2) | ( 2, 2 -3) | P'( 2,-1) |
N(3,-1) | ( 3,-1 -3) | N'( 3,-4) |
B(- 1,- 2) | (-1,- 2 -3) | B'(-1,-5) |
With these points, we are able to draw transformed image as â–ł P'N'B'.
To complete the reflection, we have to reflect all of the vertices of â–ł P'N'B' on the opposite side of the y-axis. The distance from the vertices to the y-axis remains the same. We will call the reflected image â–ł P''N''B''.
The final glide reflection is the combined translation and reflection.