Chapter 9
Section 1 – Reflections
 Reflection in a Line – maps a point to its image such that:
o If the point is on the line, then the image and preimage are the same point OR
o If the point does not lie on the line, the line is the perpendicular bisector of the
segment joining the two points.
o
1. Draw the reflection of the given figure in this line using a ruler.
2. Ticket Sales – Joy wants to select a good location to sell tickets for a dance. Locate point P such that
the distance someone would have to walk from Hallway A, to point P on the wall, and then to the next class
in Hallway B is minimized.
3. Quadrilateral JKLM has vertices J(2,3), K(3,2),L(2,-1) and M(0,1). Graph JKLM and its image in the given
line.
(a) x = 1
(b) y = -2
4. Graph each figure and its image under the given reflection.
- quadrilateral ABCD with vertices A(1,1), B(3,2), C(4, -1) and D(2, -3)
(a) under reflection in the x-axis
(b) under reflection in the y-axis
5. Quadrilateral ABCD has vertices A(1,1), B(3,2), C(4, -1) and D(2, -3). Graph ABCD and its image under
reflection in the line y = x.
Homework – Page 619 – 620 (11 – 21) ODD (24 – 29)ALL and (16, 30, 31, 45, 48)

Section 2 – Translations
Translation – maps a each point to its image along a vector, called the translation vector such that:
o Each segment joining a point and its image has the same length as the sector AND
o This segment is also parallel to the vector
1. Draw the translation of the figure along the translation vector.
(a)
(b)
2. Graph each figure and its image along the given vector.
(a) Triangle TUV with vertices
T(-1, -4), U(6, 2) and V(5, -5); <-3, 2>
(b) Pentagon PENTA with vertices
P(1,0), E(2,2), N(4,1), T(4,-1), A(2,-2); <-5,-1>
3. The graph shows repeated translations that result in the animation of the raindrop.
(a)
(a) Describe the translation of the raindrop from
position 2 to position 3 in function notation and
in words.
(b)
(b) Describe the translation of the raindrop from
position 3 to position 4 using a translation
vector
Homework – Page 627 – 628 (9, 11, 13, 14 – 24, 30)

Section 3 – Rotations
Rotation – about a fixed point, called the center of rotation, through an angle ‘x’ maps a points to its image
such that:
o If the point is the center of rotation, then the image and preimage are the same point OR
o If the point is not the center of rotation, then the image and preimage are the same distance
from the center of rotation and the measure of the angle of rotation formed by the preimage,
center of rotation, and image points is x.
1. Use a protractor and ruler to draw a rotation of the figure the given number of degrees about K.
(a)
(b)
2. Triangle DEF has vertices D(-2, -1), E(-1, 1) and F(1, -1). Graph triangle DEF and its image after a
rotation of 115 degrees clockwise about the point G(-4, -2).
3. Hexagon DGJTSR is shown below. What is the image of point T after a 90 degrees counterclockwise
rotation about the origin?
Homework – Page 635 – 636 (5 – 21) ALL
Section 4 – Compositions of Transformations
1. Triangle PQR has vertices P(1,1), Q(2,5), and R(4, 2). Graph triangle PQR and its image after the
indicated glide reflection.
(a) Translation along <-2,0>
(b) Translation along <-3, -3>
Reflection: in x-axis
Reflection: in y = x
2. Triangle ABC has vertices A(-6, 2), B(-5, -5), and C(-2, -1). Graph triangle ABC and its image after the
composition of transformations in the order listed.
(a) Translation: along <3, -1>
(b) Rotation: 180 about the origin
Reflection: in y-axis
Translation: along <-2,4>
3. Copy and reflect figure B in line ‘n’ and then line ‘q’. Then describe a single transformation that maps B
onto B”.
(a)
(b)
4. Describe the transformations that are combined to create each brick pattern shown.
4 (from book) – Describe the transformations that are combined to create each carpet pattern shown.
Homework – Page 645 – 647 (7 – 24)ALL and (34, 35)

Section 5 – Symmetry
Line Symmetry – (or reflection symmetry) is when a figure can be mapped onto itself by a reflection
in a line, called a line of symmetry (or axis of symmetry).
1. State whether the object appears to have line symmetry. Write yes or no. If so, copy the figure, draw all
lines of symmetry, and state their number.
(a)
(b)
(c )
2. State whether the figure has rotational symmetry. Write yes or no. If so, copy the figure, locate the
center of symmetry, and state the order and magnitude of symmetry.
(a)
(b)
(c )
3. State whether the figure has plane symmetry, axis symmetry, both or neither.
(a)
(b)
Homework – Page 656 – 658 (9 – 33 and 35-38)

Section 6 – Dilations
Dilation – with center ‘C’ and positive scale factor k, k ≠ 1, maps a point ‘P’ in a figure to its image
such that:
o If point P and C coincide, then the image and preimage are the same point OR
o If point P is not the center of dilation, then P’ lies on CP and CP’ = k(CP)
1. (a) To create the illusion of a “life-sized” image, puppeteers sometimes use a light source to show an
enlarged image of a puppet projected on a screen or wall. Suppose that the distance between a light
source L and puppet is 24 inches (LP). To what distance PP’ should you place the puppet from the screen
to create a 49.5-inch tall shadow (I’M’) from a 9-inch puppet?
(b) Determine whether the dilation from Figure Q to Q’ is an enlargement or a reduction. Then find the
scale factor of the dilation and x.
2. Trapezoid EFGH has vertices E(-8,4), F(-4,8), G(8,4) and H(-4,-8). Graph the image of EFGH after a
dilation centered at the origin with scale factor of ¼.
Guided Practice - 3 – DO WITH PARTNER
Homework – Page 664 – 666 (15-26, 41)