Q22. For exercises 21-23, use the fol... [FREE SOLUTION]

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Chapter 4: Q22. (page 179)

For exercises 21-23, use the following information
Parallelogram $D E F G$ with $D (2, 4), E (5, 4), F (4, 1), and G (1, 1)$ is rotated $270 掳$ counter clockwise about the origin.
22. Find the coordinates of parallelogram $D' E' F' G'$

Short Answer

Expert verified

Coordinates of the image after rotation of $270 掳$ counter clockwiseare

$D' (4, - 2), E' (4, - 5), F' (1, - 4), and G' (1, - 1)$

Step by step solution

- Vertex matrix of parallelogram DEFG

Vertex matrix of coordinates of given parallelogram is $[\begin{matrix} 2 & 5 & 4 & 1 \\ 4 & 4 & 1 & 1 \end{matrix}]$

- Vertex matrix after rotation

Vertex matrix of parallelogram after rotation of $270 掳$ counter clockwise is product of matrix $[\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}]$ with vertex matrix of given parallelogram as shown below

$[\begin{matrix} 0 & 1 \\ 鈭� 1 & 0 \end{matrix}] 脳 [\begin{matrix} 2 & 5 & 4 & 1 \\ 4 & 4 & 1 & 1 \end{matrix}] = [\begin{matrix} 4 & 4 & 1 & 1 \\ 鈭� 2 & 鈭� 5 & 鈭� 4 & 鈭� 1 \end{matrix}]$

- Coordinates of image after rotation

As, each coordinate is represented by a column of vertex matrix, so each column represents one coordinate.

Thus, coordinates of image after rotation are

$D' (4, - 2), E' (4, - 5), F' (1, - 4), and G' (1, - 1)$

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91影视

For exercises 21-23, use the following information
Parallelogram $D E F G$ with $D (2, 4), E (5, 4), F (4, 1), and G (1, 1)$ is rotated $270 掳$ counter clockwise about the origin.
22. Find the coordinates of parallelogram $D' E' F' G'$

Short Answer

Step by step solution

- Vertex matrix of parallelogram DEFG

- Vertex matrix after rotation

- Coordinates of image after rotation

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Logic and Functions

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91影视

For exercises 21-23, use the following informationParallelogram DEFG with D2,4,E5,4,F4,1,andG1,1 is rotated 270掳 counter clockwise about the origin.22. Find the coordinates of parallelogram D'E'F'G'

Short Answer

Step by step solution

- Vertex matrix of parallelogram DEFG

- Vertex matrix after rotation

- Coordinates of image after rotation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Discrete Mathematics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

For exercises 21-23, use the following information
Parallelogram $D E F G$ with $D (2, 4), E (5, 4), F (4, 1), and G (1, 1)$ is rotated $270 掳$ counter clockwise about the origin.
22. Find the coordinates of parallelogram $D' E' F' G'$