Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question:** What is the transformation matrix for reflecting over the y-axis?
**Choices:**
a) \[
\begin{pmatrix}
-1 & 0 \\
0 & 1
\end{pmatrix}
\]
b) \[
\begin{pmatrix}
0 & 1 \\
-1 & 0
\end{pmatrix}
\]
c) \[
\begin{pmatrix}
1 & 0 \\
0 & -1
\end{pmatrix}
\]
d) \[
\begin{pmatrix}
-1 & 0 \\
0 & -1
\end{pmatrix}
\]
e) \[
\begin{pmatrix}
0 & -1 \\
1 & 0
\end{pmatrix}
\]
**Explanation:**
- The transformation matrix for reflecting over the y-axis is used to flip the x-coordinate of a point across the y-axis, essentially changing the sign of the x-coordinate while keeping the y-coordinate the same.
- Option (a) \(\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\) represents the correct transformation matrix for reflecting over the y-axis.
No graphs or diagrams are included in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa19b2cf3-e4ba-4c54-87ea-4b78f08e1dba%2F17624033-bbdb-469c-99b6-176f2552e60e%2Fe6c8o9i_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:** What is the transformation matrix for reflecting over the y-axis?
**Choices:**
a) \[
\begin{pmatrix}
-1 & 0 \\
0 & 1
\end{pmatrix}
\]
b) \[
\begin{pmatrix}
0 & 1 \\
-1 & 0
\end{pmatrix}
\]
c) \[
\begin{pmatrix}
1 & 0 \\
0 & -1
\end{pmatrix}
\]
d) \[
\begin{pmatrix}
-1 & 0 \\
0 & -1
\end{pmatrix}
\]
e) \[
\begin{pmatrix}
0 & -1 \\
1 & 0
\end{pmatrix}
\]
**Explanation:**
- The transformation matrix for reflecting over the y-axis is used to flip the x-coordinate of a point across the y-axis, essentially changing the sign of the x-coordinate while keeping the y-coordinate the same.
- Option (a) \(\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}\) represents the correct transformation matrix for reflecting over the y-axis.
No graphs or diagrams are included in the image.
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