Upload
others
View
9
Download
0
Embed Size (px)
Citation preview
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?