Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Find the image of each letter for a reflection first across line ℓ bold italic script l  and then across line m. Is the resulting transformation a translation or a rotation? For a translation, describe the direction and distance. For a rotation, tell the center of rotation and the angle of rotation.

See Problem 3.

Graph Δ P N B cap delta p n b  and its glide reflection image for the given translation and reflection line.

12. ( x , y ) → ( x + 2 , y ) ; y = 3 open x comma y close rightwards arrow open x plus 2 comma y close semicolon y equals 3
13. ( x , y ) → ( x , y − 3 ) ; x = 0 open x comma y close rightwards arrow open x comma y minus 3 close semicolon x equals 0
14. ( x , y ) → ( x + 2 , y + 2 ) ; y = x open x comma y close rightwards arrow open x plus 2 comma y plus 2 close semicolon y equals x
15. ( x , y ) → ( x − 1 , y + 1 ) ; y = − x open x comma y close rightwards arrow open x minus 1 comma y plus 1 close semicolon y equals negative x

See Problem 4.

Each figure below is an isometry image of the figure below. Tell whether the two figures' orientations are the same or opposite. Then classify the isometry.

Each figure below is an isometry image of the figure below. Tell whether the two figures' orientations are the same or opposite. Then classify the isometry.

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