Chapter 4: Q8. (page 178)

For exercises 7-10, use the rectangle at the right
Find the coordinates of the image after a dilation by a scale factor of 3.

Short Answer

Expert verified

Coordinates of the image after a dilation by a scale factor of 3 are $A' (0, 12), B' (15, 12), C' (15, 0), and D' (0, 0)$

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 dilation

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 dilation is product of scale factor with vertex matrix of given rectangle as shown below

$3 \times [\begin{matrix} 0 & 5 & 5 & 0 \\ 4 & 4 & 0 & 0 \end{matrix}] = [\begin{matrix} 0 & 15 & 15 & 0 \\ 12 & 12 & 0 & 0 \end{matrix}]$

- 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

$A' (0, 12), B' (15, 12), C' (15, 0), and D' (0, 0)$

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For exercises 7-10, use the rectangle at the right
Find the coordinates of the image after a dilation by a scale factor of 3.

Short Answer

Step by step solution

- Write Coordinates of rectangle

- Vertex matrix after dilation

- Coordinates of image after dilation

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For exercises 7-10, use the rectangle at the rightFind the coordinates of the image after a dilation by a scale factor of 3.

Short Answer

Step by step solution

- Write Coordinates of rectangle

- Vertex matrix after dilation

- Coordinates of image after dilation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Statistics

Decision Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

For exercises 7-10, use the rectangle at the right
Find the coordinates of the image after a dilation by a scale factor of 3.