PQhas coordinates P(3,-6) and Q(3, 9). Find the coordinates of P'Q' after a dilation with a scale factor of centered at (3,-1). 5

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.4: Subtracting Real Numbers
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**Problem Statement:**

PQ has coordinates P(3, -6) and Q(3, 9). Find the coordinates of P'Q' after a dilation with a scale factor of \( \frac{1}{5} \) centered at (3, -1).

**Graph Explanation:**

The image includes a coordinate plane with both x and y axes labeled from -9 to 9. It is a standard Cartesian coordinate grid with a clear origin at (0,0). The grid lines provide reference points for plotting and visualizing the dilation task described in the problem.
Transcribed Image Text:**Problem Statement:** PQ has coordinates P(3, -6) and Q(3, 9). Find the coordinates of P'Q' after a dilation with a scale factor of \( \frac{1}{5} \) centered at (3, -1). **Graph Explanation:** The image includes a coordinate plane with both x and y axes labeled from -9 to 9. It is a standard Cartesian coordinate grid with a clear origin at (0,0). The grid lines provide reference points for plotting and visualizing the dilation task described in the problem.
The image shows text from an educational document on transformations in geometry. Below is the transcription suitable for an educational website:

---

**Notes:**

If there is not a single transformation that carries one figure onto the next, then we use a __________ of __________.

**What are the symbols of transformations (how will it be written)?**

- Translation: __________
- Rotation: __________
- Reflection: __________
- Dilation: __________

The symbol for the composition of transformations is an __________ o.

For example:
__________ tells us to translate \((x, y) \rightarrow (x+1, y+4)\) after a reflection about the line \(y = -1\).

A composition of isometries is a composition, or sequence, of two or more __________.

**Study Tip:**

When reading a composition of transformations in symbolism, the transformations must be performed from right to left.

\[ T_{3, 9} \circ r_{x=10} \]

Do SECOND:  \( T_{3,9} \)  __________  Do FIRST:  \( r_{x=10} \)

Page 7

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*Note: No graphs or diagrams were present in the image, only text and a small instructional tip box.*
Transcribed Image Text:The image shows text from an educational document on transformations in geometry. Below is the transcription suitable for an educational website: --- **Notes:** If there is not a single transformation that carries one figure onto the next, then we use a __________ of __________. **What are the symbols of transformations (how will it be written)?** - Translation: __________ - Rotation: __________ - Reflection: __________ - Dilation: __________ The symbol for the composition of transformations is an __________ o. For example: __________ tells us to translate \((x, y) \rightarrow (x+1, y+4)\) after a reflection about the line \(y = -1\). A composition of isometries is a composition, or sequence, of two or more __________. **Study Tip:** When reading a composition of transformations in symbolism, the transformations must be performed from right to left. \[ T_{3, 9} \circ r_{x=10} \] Do SECOND: \( T_{3,9} \) __________ Do FIRST: \( r_{x=10} \) Page 7 --- *Note: No graphs or diagrams were present in the image, only text and a small instructional tip box.*
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