Chapter 4: Q19. (page 179)

For exercises 18-20, use the following information
The vertices of $Δ X Y Z$ 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 $Δ X' Y' Z'$

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

$[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] \times [\begin{matrix} 1 & 2 & 7 \\ - 1 & - 4 & - 1 \end{matrix}] = [\begin{matrix} - 1 & - 4 & - 1 \\ 1 & 2 & 7 \end{matrix}]$

- 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

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

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For exercises 18-20, use the following information
The vertices of $Δ X Y Z$ 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 $Δ X' Y' Z'$

Short Answer

Step by step solution

- Vertex matrix of ΔXYZ

- Vertex matrix after reflection

- Coordinates of image after dilation

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

Pure Maths

Calculus

Statistics

Discrete Mathematics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

For exercises 18-20, use the following information
The vertices of $Δ X Y Z$ 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 $Δ X' Y' Z'$