Q44. Which matrix represents a reflec... [FREE SOLUTION]

Chapter 4: Q44. (page 181)

Which matrix represents a reflection over the y-axis followed by a reflection over the x-axis?
A $[\begin{matrix} 0 & - 1 \\ - 1 & 0 \end{matrix}]$ B $[\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}]$ C $[\begin{matrix} - 1 & - 1 \\ - 1 & - 1 \end{matrix}]$ D none of these

Short Answer

Expert verified

The matrix represents a reflection over the y-axis followed by a reflection over the x-axis is $B [\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}]$

Step by step solution

- Vertex matrix

Let $(x, y)$ be an ordered pair then its vertex matrix will be $[\begin{matrix} x \\ y \end{matrix}]$

- Vertex matrix after reflection over the y-axis

Vertex matrix of new point $(x_{1}, y_{1})$ after reflection over the y -axis is product matrix localid="1648210460918" $[\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}]$ with vertex matrix of original point as shown below

localid="1648210486244" $[\begin{matrix} x_{1} \\ y_{1} \end{matrix}] = [\begin{matrix} - 1 & 0 \\ 0 & 1 \end{matrix}] 脳 [\begin{matrix} x \\ y \end{matrix}]$

- Vertex matrix after reflection over the x-axis

Vertex matrix of new point $(x_{2}, y_{2})$ after reflection over the x -axis is product matrix localid="1648210501553" $[\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}]$ with vertex matrix of point localid="1648210631325" $(x_{1}, y_{1})$ and use the associative property of matrix multiplication as shown below

$\begin{matrix} [\begin{matrix} x_{2} \\ y_{2} \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 鈭� 1 \end{matrix}] 脳 [\begin{matrix} x_{1} \\ y_{1} \end{matrix}] \\ = [\begin{matrix} 1 & 0 \\ 0 & 鈭� 1 \end{matrix}] 脳 ([\begin{matrix} 鈭� 1 & 0 \\ 0 & 1 \end{matrix}] 脳 [\begin{matrix} x \\ y \end{matrix}]) \\ = ([\begin{matrix} 1 & 0 \\ 0 & 鈭� 1 \end{matrix}] 脳 [\begin{matrix} 鈭� 1 & 0 \\ 0 & 1 \end{matrix}]) 脳 [\begin{matrix} x \\ y \end{matrix}] \\ = [\begin{matrix} 鈭� 1 & 0 \\ 0 & 鈭� 1 \end{matrix}] 脳 [\begin{matrix} x \\ y \end{matrix}] \end{matrix}$

Thus, the matrix represents a reflection over the y-axis followed by a reflection over the x-axis is localid="1648210511006" $[\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}]$

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91影视

Which matrix represents a reflection over the y-axis followed by a reflection over the x-axis?
A $[\begin{matrix} 0 & - 1 \\ - 1 & 0 \end{matrix}]$ B $[\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}]$ C $[\begin{matrix} - 1 & - 1 \\ - 1 & - 1 \end{matrix}]$ D none of these

Short Answer

Step by step solution

- Vertex matrix

- Vertex matrix after reflection over the y-axis

- Vertex matrix after reflection over the x-axis

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91影视

Which matrix represents a reflection over the y-axis followed by a reflection over the x-axis?A0-1-10 B-100-1 C-1-1-1-1 D none of these

Short Answer

Step by step solution

- Vertex matrix

- Vertex matrix after reflection over the y-axis

- Vertex matrix after reflection over the x-axis

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Which matrix represents a reflection over the y-axis followed by a reflection over the x-axis?
A $[\begin{matrix} 0 & - 1 \\ - 1 & 0 \end{matrix}]$ B $[\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}]$ C $[\begin{matrix} - 1 & - 1 \\ - 1 & - 1 \end{matrix}]$ D none of these