### 9-1

```9-1 Reflections
You identified reflections.
• Draw reflections.
• Draw reflections in the coordinate plane.
Reflection
She saw her reflection in
the mirror.
The trees were reflected
in the lake.
The sphere was so clear, I
saw my reflection.
Definition of Reflection
A reflection is a flipping of a figure over a line.
This is the line of reflection. A reflection is a
special type of transformation.
Line of Reflection
Pre-Image/Image
Pre-image the original figure
Image
the figure after a transformation
A
B
B′
C
Pre-image (1)
l
C′
Image (2)
A′
Pre-image/Image
To tell the two images apart, use prime notation
A′.
When naming images of figures, list
corresponding points in the same order.
Reflective Detective
Fold a sheet of paper in half. Poke the tip of a pencil
through the folded paper at 3 points that are not
collinear.
Open the paper and draw segments connecting the holes
on each side of the fold. (You should have 2 triangles
with the fold as the line of reflection.) Label all the
points.
Draw segments connecting the points of the image with
corresponding points of the pre-image. Measure the
distance from the vertices to the fold. Measure the
angles these segments make with the fold.
Vocabulary
Equidistant
two points are the same distance
from another point, segment or line.
Bisector
a figure is cut into two congruent
halves.
Perpendicular bisector
a line or segment that
divides the segment into two congruent
segments and is perpendicular to it.
A
B
l
l is a perpendicular bisector of AB
p. 623
Reflect a Figure in a Line
Draw the reflected image of quadrilateral WXYZ in
line p.
Step 1 Draw segments
perpendicular to line p from
each point W, X, Y, and Z.
Step 2 Locate W', X', Y',
and Z' so that line p is the
perpendicular bisector of
Points W', X', Y', and Z' are
the respective images of W,
X, Y, and Z.
Step 3 Connect vertices
W', X', Y', and Z'.
Answer: Since points W', X', Y',
and Z' are the images of points
W, X, Y, and Z under reflection
W'X'Y'Z' is the reflection of
Draw the reflected image of quadrilateral ABCD in
line n.
A.
B.
C.
D.
Reflect a Figure in a Horizontal or Vertical Line
A. Quadrilateral JKLM has vertices J(2, 3), K(3, 2),
L(2, –1), and M(0, 1). Graph JKLM and its image
over x = 1.
Use the horizontal grid lines to find a corresponding point
for each vertex so that each vertex and its image are
equidistant from the line x = 1.
Reflect a Figure in a Horizontal or Vertical Line
Use the horizontal grid lines to find a corresponding point
for each vertex so that each vertex and its image are
equidistant from the line x = 1.
Reflect a Figure in a Horizontal or Vertical Line
B. Quadrilateral JKLM has vertices J(2, 3), K(3, 2),
L(2, –1), and M(0, 1). Graph JKLM and its image
over y = –2.
Use the vertical grid lines to find a corresponding point
for each vertex so that each vertex and its image are
equidistant from the line y = –2.
A. Quadrilateral ABCD has vertices A(1, 2), B(0, 1),
C(1, –2), and D(3, 0). Graph ABCD and its image
over x = 2.
A.
B.
C.
D.
p. 625
Reflect a Figure in the x- or y-axis
with vertices A(1, 1), B(3, 2),
C(4, –1), and D(2, –3) and its
image reflected in the x-axis.
Multiply the y-coordinate of each
vertex by –1.
(x, y)
→
(x, –y)
A(1, 1)
B(3, 2)
C(4, –1)
D(2, –3)
→
→
→
→
A'(1, –1)
B'(3, –2)
C'(4, 1)
D'(2, 3)
Reflect a Figure in the x- or y-axis
with vertices A(1, 1), B(3, 2),
C(4, –1), and D(2, –3) and its
reflected image in the y-axis.
Multiply the x-coordinate of each
vertex by –1.
(x, y)
→
(–x, y)
A(1, 1)
B(3, 2)
C(4, –1)
D(2, –3)
→
→
→
→
A'(–1, 1)
B'(–3, 2)
C'(–4, –1)
D'(–2, –3)
A. Graph quadrilateral LMNO with vertices L(3, 1),
M(5, 2), N(6, –1), and O(4, –3) and its reflected
image in the x-axis. Select the correct coordinates
A. L'(3, –1), M'(5, –2),
N'(6, 1), O'(4, 3)
B. L'(–3, 1), M'(–5, 2),
N'(–6, –1), O'(–4, –3)
C. L'(–3, –1), M'(–5, –2),
N'(–6, 1), O'(–4, 3)
D. L'(1, 3), M'(2, 5),
N'(–1, 6), O'(–3, 4)
p. 626
Reflect a Figure in the Line y = x
A(1, 1), B(3, 2), C(4, –1), and
D(2, –3). Graph ABCD and its
image under reflection of the line
y = x.
Interchange the x- and y-coordinates
of each vertex.
(x, y)
→
(y, x)
A(1, 1)
B(3, 2)
C(4, –1)
D(2, –3)
→
→
→
→
A'(1, 1)
B'(2, 3)
C'(–1, 4)
D'(–3, 2)