Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Let's break down the composition of transformations given in the question to understand which rule correctly maps the pre-image \( PQRS \) to the image \( P'Q'R'S'' \).
### Transformations
1. Rotation \( R_{0, 270^\circ} \):
- This denotes a rotation of \( 270^\circ \) (counterclockwise) about the origin.
- Generally, rotating \((x, y)\) by \( 270^\circ \) counterclockwise about the origin results in \((y, -x)\).
2. Translation \( T_{-2,0} \):
- This denotes a translation by \(-2\) units along the x-axis.
- Translating \((x, y)\) by \(-2\) units along the x-axis changes the coordinates to \((x-2, y)\).
3. Reflection \( r_{y-2,xis(i)} \):
- Reflection across a line. However, since the parameters seem a bit off, for simplicity, consider typical reflection behaviors.
### Composition Rules
- When composing transformations, the order in which you apply them is crucial. \( A \circ B \) means you apply \( B \) first and then \( A \).
#### Let's analyze each option with some hypothetical points:
1. \( R_{0, 270^\circ} \circ T_{-2,0}(x, y) \):
- First translate \((x, y)\) to \((x-2, y)\).
- Then apply the \( 270^\circ \) rotation on \((x-2, y)\):
- Resulting in \((y, -(x-2)) = (y, -x + 2)\).
2. \( T_{-2,0} \circ R_{0, 270^\circ}(x, y) \):
- First apply the \( 270^\circ \) rotation on \((x, y)\):
- Rotation gives \((y, -x)\).
- Then translate \((y, -x)\) by \(-2\) units along the x-axis:
- Resulting in \((y-2, -x)\).
3. \( R_{0, 270^\circ} \circ r_{y-2 \cdot i \cdot s}(x, y) \):
- First reflect \((x, y)\) (parameter issue, assuming some reflection).
- Then apply the \( 270^\circ \) rotation.
4. \( r_{y-2 \cdot x \cdot i \cdot s} \circ R_{0, 270^\circ}(x, y) \):
- First apply the \( 270^\circ \) rotation on \((x, y)\):
- Giving \((y, -x)\).
- Then reflect (parameter issue, assume some reflection).
### Solution
From the detailed transformations and composition rules:
- The correct way to read and perform the transformations is: First rotation followed by translation or vice versa.
Thus, Option 2:
\( T_{-2,0} \circ R_{0, 270^\circ}(x, y) \) describes the correct composition:
First, apply the [tex]\( 270^\circ \)[/tex] rotation and then translate the result by [tex]\(-2\)[/tex] units along the x-axis.
### Transformations
1. Rotation \( R_{0, 270^\circ} \):
- This denotes a rotation of \( 270^\circ \) (counterclockwise) about the origin.
- Generally, rotating \((x, y)\) by \( 270^\circ \) counterclockwise about the origin results in \((y, -x)\).
2. Translation \( T_{-2,0} \):
- This denotes a translation by \(-2\) units along the x-axis.
- Translating \((x, y)\) by \(-2\) units along the x-axis changes the coordinates to \((x-2, y)\).
3. Reflection \( r_{y-2,xis(i)} \):
- Reflection across a line. However, since the parameters seem a bit off, for simplicity, consider typical reflection behaviors.
### Composition Rules
- When composing transformations, the order in which you apply them is crucial. \( A \circ B \) means you apply \( B \) first and then \( A \).
#### Let's analyze each option with some hypothetical points:
1. \( R_{0, 270^\circ} \circ T_{-2,0}(x, y) \):
- First translate \((x, y)\) to \((x-2, y)\).
- Then apply the \( 270^\circ \) rotation on \((x-2, y)\):
- Resulting in \((y, -(x-2)) = (y, -x + 2)\).
2. \( T_{-2,0} \circ R_{0, 270^\circ}(x, y) \):
- First apply the \( 270^\circ \) rotation on \((x, y)\):
- Rotation gives \((y, -x)\).
- Then translate \((y, -x)\) by \(-2\) units along the x-axis:
- Resulting in \((y-2, -x)\).
3. \( R_{0, 270^\circ} \circ r_{y-2 \cdot i \cdot s}(x, y) \):
- First reflect \((x, y)\) (parameter issue, assuming some reflection).
- Then apply the \( 270^\circ \) rotation.
4. \( r_{y-2 \cdot x \cdot i \cdot s} \circ R_{0, 270^\circ}(x, y) \):
- First apply the \( 270^\circ \) rotation on \((x, y)\):
- Giving \((y, -x)\).
- Then reflect (parameter issue, assume some reflection).
### Solution
From the detailed transformations and composition rules:
- The correct way to read and perform the transformations is: First rotation followed by translation or vice versa.
Thus, Option 2:
\( T_{-2,0} \circ R_{0, 270^\circ}(x, y) \) describes the correct composition:
First, apply the [tex]\( 270^\circ \)[/tex] rotation and then translate the result by [tex]\(-2\)[/tex] units along the x-axis.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
