Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
4. Compositions of Isometries
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Exercise 14 Page 574

First perform the translation and then the reflection.

Practice makes perfect

Let's first identify the coordinates of â–ł PNB.

To complete a glide reflection, we first perform the translation and then the reflection.

Translation

To translate â–ł PNB two units right and two units up, we have to add 2 to each x-coordinate and y-coordinate.

(x,y) → (x +2,y +2) Let's do this for the three vertices.

(x,y) (x +2,y +2) (x',y')
P(2, 2) ( 2 +2, 2 +2) P'(4,4)
N(3,-1) ( 3 +2,-1 +2) N'(5,1)
B(- 1,- 2) (-1 +2,- 2 +2) B'(1,0)

With these points, we are able to draw the transformed image as â–ł P'N'B'.

Reflection

To complete the reflection, we have to reflect all the vertices of â–ł P'N'B' on the opposite side of the x-axis. The distance from the vertices to the x-axis remains the same. We will call the reflected image â–ł P''N''B''.

Final Glide Reflection

The final glide reflection is the combination of the translation and the reflection.