Reflect quadrilateral DABC over the X-axis:
D(3,7)
A (3,4)
(3,-7)
(3,-4)
C (6,7)
B (6,4)
(6,-7)
(6,-4)
Transformation
a change in the position, shape, or size of a geometric
figure
Image
the resulting point or set of points of a transformation
P‘ (image)
P
Isometry
a transformation that preserves length
Mapping
replication of a point or set of points
Orientation
the arrangement of points, relative to one
another, after a transformation has occurred
A
B
C‘
C
D
D‘
A‘
B‘
Isometry-a transformation that preserves length
Orientation-the arrangement of points, relative to one
another, after a transformation has occurred
Are the transformations below an isometry? Do the
figures have the same or opposite orientation?
Isometry
Opposite orientation
Not an isometry
Same orientation
Reflection-a flip that results in a figure and its image
having opposite orientations
Every point is the same distance from the central line
The reflection has the same size as the original image
Reflect across x-axis
Triangle: A (3,3), B(4,-6), C(-2,1)
3 -3
A’ (___,___)
4 6
B’ (___,___)
-2 -1
C’ (___,___)
Rule: rx−axis (x,y) = (__,__)
x -y
B’
A
C
C’
Reflect across y-axis
Triangle: A (2, 4), B(-3, 7), C(1, 1)
A’ (___,___)
-2 4
B’ (___,___)
3 7
C’ (___,___)
-1 1
-x y
Rule: ry−axis (x,y) = (__,__)
B’
B
C’
A’
B
A
A’
C
Reflect over line y=x
Triangle: A (1,2), B(6,3), C(5,7)
2 1
A’ (___,___)
3 6
B’ (___,___)
7 5
C’ (___,___)
Rule: ry=x (x, y) = (__,__)
y x
B’
A
Reflect over line y=-x
Triangle: A (3,3), B(7,3), C(5,8)
A’ (___,___)
-3 -3
B’ (___,___)
-3 -7
C’ (___,___)
-8 -5
-y -x
Rule: ry=−x (x,y) = (___,___)
C
C
C’
B
A
A’
A’
C’
B’
B
Point A is located at (3, -9). The point is reflected in the x-axis.
Its image is located at…
(3, 9)
What is the image of point (4, -7) after the transformation
𝑟𝑦−axis ?
(-4, -7)
What is the image of (-8, 6) under the transformation 𝑟y=𝑥 ?
(6, -8)
Find the coordinates of the image of point (2, 5) after a
reflection in the line y=-x.
(-5, -2)
Reflecting over vertical lines
Triangle: A (-6,4), B(-3,2), C(5,7)
Reflect over the line x=-2
A’ (___,___)
2 4
B’ (___,___)
-1 2
C’ (___,___)
-9 7
Find the distance between the X
coordinate and the X line
Reflecting over horizontal lines
Triangle: A (4, 9), B(9, 8), C(6, 5)
Reflect over the line y=2
0 8
A’ (___,___)
-5 7
B’ (___,___)
-2 5
C’ (___,___)
Find the average between the y
coordinate and the y line
A
C
C’
A’
A
B
B’
The line is
the
midpoint
between
the point
and its
image!
B
C
C’
A’
B’
Write a rule to describe each transformation.
(Which line is the figure being reflected on?)
𝑟𝑥−𝑎𝑥𝑖𝑠 is the line
𝑟𝑥=2 is the line
The line y = 1.5x – 2 is reflected in the line y = 1. What is
the equation of the image?
y = - 1.5x + 4
The answer from question (1) is reflected in the line x =
4. What is the equation of the image?
y = 1.5x – 8
What is the line perpendicular from the answer of
question (2) passing through a point of (-3, 7)?
y=-
2
x
3
+5
Summary:
Summary:
Reflection-flip in which image has opposite orientation
Reflection-flip in which image has opposite orientation
n which image has opposite orientation
Reflection-flip
in which image hasTransformationopposite
orientation
A change in position, shape or size of a
Transformation- A change in position, shape or
size of a
- A change
in position, shape or size
of a
Transformationa
change
in
position,
shape
geometric figure or size of a geometric figure
geometric figure
e
Reflection over
x-axis
Point
(x,y)
(line of
reflects
to
reflection: xpoint
(x,-y)
axis)
Point (x,y)
reflects to
point (x,-y)
Reflection over
x-axis
(line of
reflection: xaxis)
Point (x,y)
reflects to
point (x,-y)
(line of reflection:
(line of reflection:
y-axis)
y-axis)
Reflection over line y=x or y=-x
Reflection over line y=x or y=-x
Reflection over
Reflection
y=xover
y=x
Point (x,y)
Point (x,y)
reflects to point
reflects to
point
(y,x)
(y,x)
Reflectio
Reflection
over line
over liney=-x
y=-x
Point (x,y
Point (x,y)
reflects t
reflects to
point (-y
point (-y,-x)