Name______Date______Period ______
Geometry – Easter Break AssignmentMs. Hahl
Directions: While completing your Transformation Packets, place your answers in the spaces provided below. For any part two questions (Point Reflections & Translations) you must show all work on the back of this paper. NO WORK = NO CREDIT! This assignment is due Monday April 12th. You must hand this sheet of paper in to the Math Office (E114) before 8:30 AM in the designated “Ms. Hahl” box. Absolutely no late assignments will be accepted. This assignment will be graded as a quiz. If you have any questions please e-mail me.
Line Symmetry
1. 2. 3. 4.
Point Symmetry
5. 6. 7. 8. 9.
Line ReflectionsPoint ReflectionsTranslations
1.) ______1.) ______1.) ______2.) ______2.) ______2.) ______
3.) ______3.) ______3.) ______
4.) ______4.) ______
5.) ______
6.) ______
DilationsRotations
1.) ______1.) ______
2.) ______2.) ______
3.) ______3.) ______
4.) ______4.) ______
Name______Date______Period ______
Geometry – Easter Break AssignmentMs. Hahl
Directions: This packet is to be completed by you over Easter break. All answers are to be placed on the provided answer sheet, with necessary work on the back. This assignment is due Monday April 12th. You must hand in the answer sheet to the Math Office (E114) before 8:30 AM in the designated “Ms. Hahl” box. Absolutely no late assignments will be accepted. This assignment will be graded as a quiz. If you have any questions please e-mail me.
Transformations
A transformation occurs when the size or position of an original figure is changed.
An algebraic rule, called a mapping, defines a transformation by assigning ordered pairs of the
coordinate plane to new locations
If the points of a given figure are labeled with letters such as A, B, and C, then their
transformation image has points labeled with the same letter and a prime sign (‘), such as A’,
B’ and C’. The original points are called the pre-image.
Line Symmetry
If a figure has line symmetry, a line can be drawn through the figure such that both sides of the
figure are “mirror images” of each other. Such a line is called the axis of symmetry.
A figure may have more than one line of symmetry or no lines of symmetry.
Example: Given the shape on the right, draw the line(s) of symmetry.
Do Now: Draw the line(s) of symmetry in each figure.
1. 2. 3. 4.
Point Symmetry
A figure is said to have point symmetry if the figure coincides with itself when rotated 180°
about a point. This point is called the point of symmetry.
(To determine if a figure has point symmetry, turn it upside down. If it’s in the same position as
it originally was, it has point symmetry)
Do Now: Determine if each figure below has point symmetry. (Write Yes or No)
5. 6. 7. 8. 9.
Line Reflections
A line reflection is a transformation in which a figure is reflected over a given line as if in a mirror.
Each point of the reflection image is the same distance from the line of reflection as
the point from the original figure.
Line Reflection Mapping Rules
A.) A reflection in the x-axis
P(x,y)P’(x, -y) (Look at what happened to the point: x stayed the same
and y became negative.)
B.) A reflection in the y-axis
P(x,y)P’(-x, y) (Look at what happened to the point: x became negative
and y stayed the same.)
C.) A reflection in the line y = x
P(x,y)P’(y, x) (Look at what happened to the point: the x and y
switched places.)
D.) A reflection in the line y = -x
P(x,y)P’(-y, -x) (Look at what happened to the point: x and y switched
places and both became negative.)
E.) A reflection in the line x = k. (Any vertical line)
P(x,y)P’(2k-x,y)
F.) A reflection in the line y = k. (Any horizontal line)
P(x,y)P’(x, 2k-y)
Example: Reflect the point (2, -1) in each line below. (Use the rules above)
1.) In the y-axis: (2,-1) (-2,-1)
2.) In the x-axis: (2,-1) (2,1)
3.) In the line y = x: (2,-1) (-1,2)
4.) In the line y = -x: (2,-1) (1,-2)
5.) In the line x = 3: (2,-1) (2(3)-2, -1) = (4, -1)
6.) In the line y = 6: (2,-1) (2, 2(6)- -1) = (2, 13)
Do Now: Reflect each point below in the given line.
1.) A(6,7) ______2.) B(-3,3) ______
3.) C(-1,2) ______4.) D(9,2) ______
5.) E (3,-5) ______6.) F(-7,5) ______
Point Reflections
If a figure is reflected through point P, then P is the midpoint of the line segment joining a
point to its image.
Point Reflection Mapping Rules:
*Must use midpoint formula*
The point of reflection is the midpoint of a given point and its image.
Label the point of reflection (, ) Label the given point (, ) and its image (,)
Example 1: What is the image of A(3,5) under a reflection in the point (-1, 2)
(Here the point of reflection (-1,2) is the midpoint and (3,5) is the given point)
Write the formula
Substitute
(-2 = , 4 = ) Cross multiply and Solve for x and y
Answer: A’(-5,-1)
Example 2: What is the point of reflection that maps A(2,-6) to A’(10,4)?
(Here you are looking for the midpoint which is the point of reflection)
Write the formula
Substitute and simplify
Answer: Point of Reflection: (6,-1)
Do Now:
1.) Find the image of the point R(-7,1) under a reflection in the point (0,0).
2.) What is the image of A(8,1) under a reflection in the point (4, 1)?
3.) What is the point of reflection that maps B(2,2) to B’(-3,4)?
4.) What is the point of reflection that maps D(7,3) to B’(1,-3)?
Translations
A translation is a transformation in which a figure slides a certain distance.
Translation Mapping Rule:
(x,y) (x+a, y+b)Add the first number to the x and the second number to y
Example: What is the image of A(-2,1) under the transformation ?
A(-2,1) A’(-2+5, 1+-1)
A’(3,0)
Do Now:
1.) What is the image of B(9,3) under the transformation ?
2.) What is the image of C(8,0) under the transformation ?
3.) What is the image of D(-1,-3) under the transformation ?
Dilations
A dilation is a transformation in which the size of a figure is changed and the figure is moved.
The constant of dilation is also called the scale factor.
Dilation Mapping Rule:
(x,y) (kx, ky) (Multiply each coordinate by the scale factor)
Example: Find the image of A(2,-4) under a dilation of 5.
A(2,-4) A’(5(2),5(-4))
A’ (10, -20)
Do Now:
1.) B(6,-3) ______2. G(-2,6) ______
3.) C(3,12) ______4. D(-1,-5) ______
Rotations
A rotation is a transformation in which a figure is turned around a point called the point of rotation.
- Counterclockwise rotations are positive
- Clockwise rotations are negative
Rotation Mapping Rules:
1.) Rotation of 90° and Rotation of -270°
(x,y) (-y,x) and (x,y) (-y,x) (It’s the same rule for both rotations)
2.) Rotation of 180° and Rotation of -180°
(x,y) (-x,-y) and (x,y) (-x,-y) (It’s the same rule for both rotations)
3.) Rotation of 270° and Rotation of -90°
(x,y) (y,-x) and (x,y) (y,-x) (It’s the same rule for both rotations)
4.) Rotation of 360° and Rotation of -360°
(x,y) (x,y) and (x,y) (x,y) (It’s the same rule for both rotations)
Example: Rotate the following points
1.) (6,2) (-2,6)2.) (7,-5) (-5,-7)
3.) (12,4) (-12,-4)4.) (-6,2) (-6,2)
Do Now:
1.) (-5,-2) ______2.) (6,-1) ______
3.) (-2,-3) ______4.) (8,5) ______