1. The vertices of ΔABC are A(−5,4), B(−2,4), and C(−4,2). If ΔABC is reflected across the y-axis to produce the image ΔA′B′C′, find the coordinates of the vertex C′.
2. The vertices of trapezoid ABCD are A(3,−3), B(5,−3), C(6,−5), and D(1, −5). Draw a graph which shows ABCD and A′B′C′D′ after a reflection across the y-axis.
3.
a. The vertices of ΔABC are A(−5,5), B(−2,4), and C(−2,3). Draw a graph which shows ΔABC and its reflection across the x-axis, ΔA′B′C′.
b. Graph the reflection of ΔA′B′C′ across the y-axis.
4.
a. Writing Which of the figures are reflections of the parallelogram ABCD?
b. Describe the reflections in words.
5. Reasoning One image of ΔABC is A′B′C′.
a. How do the x-coordinates of the vertices change?
b. How do the y-coordinates of the vertices change?
c. What type of reflection is the image ΔA′B′C′?
6. Think About the Process
a. What is true about a figure and an image created by a reflection? Select all that apply.
A. They are the same size.
B. The figure and the image are the same shape.
C. Each point on the image has the same x-coordinate as the corresponding point in the figure.
D. Each point on the image moves the same distance and direction from the figure.
b. One image of ABCD is A′B′C′D′. What type of reflection is the image A′B′C′D′?
7. Error Analysis Your friend incorrectly says that the reflection of ΔEFG to its image ΔE′F′G′ is a reflection across the x-axis.
a. What is the correct description of the reflection?
b. What is your friend′s mistake?