Reflections
Warm Up:
Reflect quadrilateral ABCD over the X-axis:
A(3,7)
B (6,7)
D (3,4)
C (6,4)
Practice Questions
Are the transformations below an isometry? Do the figures have the same or
opposite orientation?
1.
2.
Isometry? _________________
Orientation? _________________
Isometry? _________________
Orientation? _________________
3. Reflect across the x-axis
Triangle: A (3,3), B(4,-6), C(-2,1)
A’ (___,___)
B’ (___,___)
C’ (___,___)
Rule: r
(x,y) = (__,__)
5.
Reflect over line y=x
Triangle: A (1,2), B(6,3), C(5,7)
A’ (___,___)
B’ (___,___)
C’ (___,___)
Rule: r (x, y) = (__,__)
4. Reflect across the y-axis
Triangle: A (2, 4), B(-3, 7), C(1, 1)
A’ (___,___)
B’ (___,___)
C’ (___,___)
Rule: r
(x,y) = (__,__)
6. Reflect over line y=-x
Triangle: A (3,3), B(7,3), C(5,8)
A’ (___,___)
B’ (___,___)
C’ (___,___)
Rule: r =
(x,y) = (___,___)
Regents Questions
Point A is located at (3, -9). The point is reflected in the x-axis. Its image is
located at…
What is the image of point (4, -7) after the transformation
What is the image of (-8, 6) under the transformation
?
?
Find the coordinates of the image of point (2, 5) after a reflection in the line y=-x.
Practice Questions
1. Reflect over vertical lines (x=-2)
2. Reflect over horizontal line (y=2)
Triangle: A (-6,4), B(-3,2), C(5,7)
A’ (___,___)
B’ (___,___)
C’ (___,___)
Rule: Find the average between
the X coordinate and the X line
Triangle: A (4, 9), B(9, 8), C(6, 5)
A’ (___,___)
B’ (___,___)
C’ (___,___)
Rule: Find the average between the
y coordinate and the y line
Write a rule to describe each transformation.
(Which line is the figure being reflected on?)
3.
4.
Challenge
ALGEBRA:
1) The line y = 1.5x – 2 is reflected in the line y = 1. What is the equation of the
image?
2) The answer from question (1) is reflected in the line x = 4. What is the
equation of the image?
3) What is the line perpendicular from the answer of question (2) passing
through a point of (-3, 7)?
Summary:
Reflection-flip in which image has opposite orientation
Transformation- A change in position, shape or size of a geometric figure
Reflection over x-axis
(line of reflection: x-axis)
Point (x,y)
reflects to point
(x,-y)
Reflection over
y-axis
(line of reflection:
y-axis)
Point (x,y) reflects
to point (-x,y)
Reflection over line y=x or y=-x
Reflection over
y=x
Point (x,y)
reflects to point
(y,x)
Reflection
over line
y=-x
Point (x,y)
reflects to
point (-y,x)
Homework
Fill in the blanks
1) Every point is the
distance from the central line
2) The reflection has the same
as the original image
Draw the reflections for the given shape and write the points below
3) reflect over both the x and y axis
(5,8)
a) X axis reflection
B
A’ (
,
)
B’ (
,
)
A
C
C’ (
,
)
(2,3)
(8,3
b) Y axis reflection
)
)
A’’(
,
)
B’’(
,
)
C’’(
,
)
True or False
4) The image of the point (8, -2) under a reflection across the x axis is (-8,-2)
______
5) The image of the point (-7,4) under a reflection under the y axis is (7,4)
______
State which line the shape is reflected over
6)
7)
Complete the rule (fill in the blanks)
8) When reflecting over the x-axis, the
coordinate becomes negative
and the
coordinate stays the same
9) When reflecting over the y-axis, the
coordinate becomes negative
and the
coordinate stays the same
Graph the Reflections over the line given
10) y=1
Homework Answers
Fill in the blanks
1) Every point is the same distance from the central line
2) The reflection has the same size
as the original image
Draw the reflections for the given shape and write the points below
3) reflect over both the x and y axis
(5,8)
a) X axis reflection
B
A’ ( 2 , -3 )
B’ ( 5 , -8 )
C’ ( 8 , -3 )
A
C
b) Y axis reflection
(2,3)
(8,3)
A’’( -2 , 3 )
)
B’’ ( -5 , 8 )
C’’( -8 , 3 )
True or False
4) The image of the point (8, -2) under a reflection across the x axis is (-8,-2)
False
5) The image of the point (-7,4) under a reflection under the y axis is (7,4)
True
State which line the shape is reflected over
6)
Y=2
7)
X=-Y
Complete the rule (fill in the blanks)
7) When reflecting over the x-axis, the Y
coordinate becomes negative
and the X coordinate stays the same
8) When reflecting over the y-axis, the X
coordinate becomes negative
and the Y coordinate stays the same
Graph the Reflections over the line given
9) y=1