Q19. For exercises 18-20, use the fol... [FREE SOLUTION]

91影视

Chapter 4: Q19. (page 179)

For exercises 18-20, use the following information
The vertices of $螖 X Y Z$ are $X (1, - 1), Y (2, - 4), and Z (7, - 1)$ . The triangle is reflected over the line \[y=x\]
19. Find the coordinates of $螖 X' Y' Z'$

Short Answer

Expert verified

Coordinates of the image after a dilation by a scale factor of 3 are $X' (- 1, 1), Y' (- 4, 2), and Z' (- 1, 7)$

Step by step solution

- Vertex matrix of ΔXYZ

Vertex matrix of coordinates of given triangle is $[\begin{matrix} 1 & 2 & 7 \\ - 1 & - 4 & - 1 \end{matrix}]$

- Vertex matrix after reflection

Vertex matrix of triangle after reflection over the line $y = x$ is product of matrix $[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$ with vertex matrix of given triangle as shown below

$[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] 脳 [\begin{matrix} 1 & 2 & 7 \\ 鈭� 1 & 鈭� 4 & 鈭� 1 \end{matrix}] = [\begin{matrix} 鈭� 1 & 鈭� 4 & 鈭� 1 \\ 1 & 2 & 7 \end{matrix}]$

- Coordinates of image after dilation

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

Thus, coordinates of image after dilation are

$X' (- 1, 1), Y' (- 4, 2), and Z' (- 1, 7)$

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 18-20, use the following information
The vertices of $螖 X Y Z$ are $X (1, - 1), Y (2, - 4), and Z (7, - 1)$ . The triangle is reflected over the line \[y=x\]
19. Find the coordinates of $螖 X' Y' Z'$

Short Answer

Step by step solution

- Vertex matrix of ΔXYZ

- Vertex matrix after reflection

- Coordinates of image after dilation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Applied Mathematics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

91影视

For exercises 18-20, use the following informationThe vertices of 螖XYZ are X1,-1,Y2,-4,andZ7,-1. The triangle is reflected over the line \[y=x\]19. Find the coordinates of 螖X'Y'Z'

Short Answer

Step by step solution

- Vertex matrix of ΔXYZ

- Vertex matrix after reflection

- Coordinates of image after dilation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Applied Mathematics

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For exercises 18-20, use the following information
The vertices of $螖 X Y Z$ are $X (1, - 1), Y (2, - 4), and Z (7, - 1)$ . The triangle is reflected over the line \[y=x\]
19. Find the coordinates of $螖 X' Y' Z'$