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 $180 °$

Short Answer

Expert verified

Coordinates of the image after a rotation of $180 °$ 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 $180 °$ is product matrix $[\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}]$ with vertex matrix of given rectangle as shown below

$[\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}] \times [\begin{matrix} 0 & 5 & 5 & 0 \\ 4 & 4 & 0 & 0 \end{matrix}] = [\begin{matrix} 0 & - 5 & - 5 & 0 \\ - 4 & - 4 & 0 & 0 \end{matrix}]$

- 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

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

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

Short Answer

Step by step solution

- Write Coordinates of rectangle

- Vertex matrix after rotation

- Coordinates of image after rotation

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

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

Decision Maths

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

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 $180 °$