Chapter 4: Q9. (page 178)

For exercises 7-10, use the rectangle at the right
9. Find the coordinates of the image after a reflection over the $x$ -axis

Short Answer

Expert verified

Coordinates of the image after a reflection over x axis 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 reflection

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 reflection over the x -axis 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 reflection

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

Thus, coordinates of image after reflection 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
9. Find the coordinates of the image after a reflection over the $x$ -axis

Short Answer

Step by step solution

- Write Coordinates of rectangle

- Vertex matrix after reflection

- Coordinates of image after reflection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

For exercises 7-10, use the rectangle at the right9. Find the coordinates of the image after a reflection over the x-axis

Short Answer

Step by step solution

- Write Coordinates of rectangle

- Vertex matrix after reflection

- Coordinates of image after reflection

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Pure Maths

Calculus

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

For exercises 7-10, use the rectangle at the right
9. Find the coordinates of the image after a reflection over the $x$ -axis