Q10. For exercises 7-10, use the rect... [FREE SOLUTION]

91影视

Chapter 4: Q10. (page 178)

For exercises 7-10, use the rectangle at the right
10. Find the coordinates of the image after a rotation of $180 掳$

Short Answer

Expert verified

Coordinates of the image after a rotation of $180 掳$ are $A' (0, - 4), B' (- 5, - 4), C' (- 5, 0), and D' (0, 0)$

Step by step solution

- Write Coordinates of rectangle

From given image, coordinates of the vertices of rectangle are $A (0, 4), B (5, 4), C (5, 0), and D (0, 0)$

- Vertex matrix after rotation

Vertex matrix of given rectangle is $[\begin{matrix} 0 & 5 & 5 & 0 \\ 4 & 4 & 0 & 0 \end{matrix}]$

So vertex matrix of new rectangle after rotation of $180 掳$ is product matrix $[\begin{matrix} 鈭� 1 & 0 \\ 0 & 鈭� 1 \end{matrix}]$ with vertex matrix of given rectangle as shown below

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

- 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

$A' (0, - 4), B' (- 5, - 4), C' (- 5, 0), and D' (0, 0)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

For exercises 7-10, use the rectangle at the right
10. Find the coordinates of the image after a rotation of $180 掳$

Short Answer

Step by step solution

- Write Coordinates of rectangle

- 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

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

91影视

For exercises 7-10, use the rectangle at the right10. Find the coordinates of the image after a rotation of 180掳

Short Answer

Step by step solution

- Write Coordinates of rectangle

- 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

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

For exercises 7-10, use the rectangle at the right
10. Find the coordinates of the image after a rotation of $180 掳$