4. Compositions of Isometries
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First perform the translation and then the reflection.
Let's first identify the coordinates of â–³ PNB.
To complete a glide reflection, we first perform the translation and then the reflection.
To translate â–³ PNB three units down, we have to subtract 3 from each y-coordinate.
| (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–³ P'N'B'.
To complete the reflection, we have to reflect all of the vertices of â–³ 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–³ P''N''B''.
The final glide reflection is the combined translation and reflection.