Compositions- Day 5

Point A is located at (4,-7). The point is reflected

in the x-axis. Its image is located at

1) (-4,7)

2) (-4,-7)

3) (4,7)

4) (7,-4)

If point (5, 2) is rotated counterclockwise 90°

about the origin, its image will be point

1) (2, 5)

2) (2, −5)

3) (−2, 5)

4) (−5, −2)

What is the image of the point (−5,2) under the

translation T(3,−4)?

1) (−9,5)

2) (−8,6)

3) (−2,−2)

4) (−15,−8)

Point J has coordinates (5,2). What would the

points be if it was dilated by a scale factor of 2.

a) (7, 4)

b) (3, 0)

c) (10, 4)

d) (2.5, 1)

Warm-Up

Composition of Transformations: the result when _____ or more transformations are combined to

produce a single transformation. An example is a _____________________.

When a _________________ (a slide or glide) and a reflection are performed one after the other, a

transformation called a ________________ is produced. In a glide reflection, the line of reflection

is ________________to the direction of the translation. It does not matter whether you glide first

and then reflect, or reflect first then glide. This transformation is ___________________. Since

translations and reflections are both isometries, a glide reflection is also an isometry.

1) Does this depict a glide reflection?

2) Which Compositions are glide reflections?

T ₅,₀ ◦ rₓ

T ₃,₂ ◦ rₓ

T ₀,₄ ◦ ry

T ₄,₄ ◦ ry=x

3) Examine the graph below. Is triangle A"B"C" a glide reflection of

triangle ABC?

Guided Problem

Practice Problem #1

Practice Problem #2

Summary Composition of transformation: When two or more transformations are

combined to produce a single transformation

Glide formation: When a figure is translated then reflected.

A Composition can be combination of two or more transformations

-Reflection

-Translation

-Rotation

-Dilation

-Symmetry

Challenge!

If all points on the line 2y =x +3 are transformed by the rule

R270 ◦ r y=-x Then what is the perpendicular slope of the new

line?

Exit ticket

If the coordinates of point A are (−2,3), what is the image of A under Ry − axis D3?

1) (−6,−9)

2) (9,−6)

3) (5,6)

4) (6,9)

Practice! Practice! Practice!

Good Job

Everyone!

Compositions Homework Name: Date:

1. A glide reflection is the result of .

a. A translation

b. A reflection

c. A rotation and a reflection performed one after the other

d. A translation and a reflection performed one after the other

2. If the coordinates of A are (3, 5), what are the coordinates of (r x-axis ₀ D2) (A)?

a. (6,-10)

b. (-10,6)

c. (-6,10)

d. (-6,-10)

3. The endpoints of line RS are R(7,−1) and S(2,−9). After the composition:

Reflection in the y−axis

Rotation 90⁰ about the origin.

What are the points of R and S?

a. R`(−7,−1),S`(−2,−9) ; R``(−9,2),S``(−1,7)

b. R`(−7,−1),S`(2,−9) ; R``(−1,−7),S``(−9,−2)

c. R`(-7,−1),S`(-2,−9) ; R``(1,-7),S``(9,−2)

d. R`(7,−1),S`(−2,−9) ; R``(−9,2),S``(7,−1)

4. Which glide reflection could map M’N’P’?

a. Translation: (x, y) to (-2,-7)

Reflection: in y-axis

b. Translation: (x, y) to (-2,-7)

Reflection: in x-axis

c. Translation: (x, y) to (-7,-2)

Reflection: in y=x

d. Translation: (x, y) to (2,7)

Reflection: y=-x

5. The point R(-3,-7) is translated so that (x, y) to (x+5, y) and then reflected in the line y=-

4. Find the coordinates of its image, R’.

a. (-10,-1)

b. (2,-1)

c. (-10, 1)

d. (-2,1)

6. In the accompanying diagram, point A has coordinates (4, 3). What are the coordinates

of A1, rₓ ₌ ₂ 0 r ₓ ₌ ₆ (A)?

7. If the coordinates of P are (2,-3), the (R90◦ 0 R180◦) (P) is

a. (-2,-3)

b. (-3,-2)

c. (3,-2)

d. (-2,3)

8. The vertices of PQR are P (1, 3), Q (8, 0), and R (7, 5). Graph the image of PQR after its

translation (x, y) (x + 3, y − 6) and its rotation 90⁰ about the origin.

9. The vertices of ABC are A (3, 4), B (5, 8), and C (10, 3). What are the coordinates of the

vertices of A’B’C’ after the transformation, r y-axis ₀ T0,-6?

10. ST has vertices S(-2, 2) and T (4,-1). What is the image of ST after the glide reflection,

r x-axis ○ T-3,0?