Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To solve this problem, we need to apply transformations to the initial vertices [tex]\( B(-3, 0), C(2, -1), D(-1, 2) \)[/tex] and see which sequence leads us to [tex]\( B^{\prime \prime}(-2,1), C^{\prime \prime}(3,2), D^{\prime \prime}(0,-1) \)[/tex].
Let's check the options provided step by step.
### Option 1: [tex]\((x, y) \rightarrow (x, -y) \rightarrow (x+1, y+1)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (x, -y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(-3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(2, 1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(-1, -2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+1, y+1)\)[/tex]
- [tex]\( B'(-3, 0) \rightarrow B^{\prime \prime}(-2, 1) \)[/tex]
- [tex]\( C'(2, 1) \rightarrow C^{\prime \prime}(3, 2) \)[/tex]
- [tex]\( D'(-1, -2) \rightarrow D^{\prime \prime}(0, -1) \)[/tex]
As a result, we obtain the vertices:
- [tex]\( B^{\prime \prime}(-2, 1) \)[/tex]
- [tex]\( C^{\prime \prime}(3, 2) \)[/tex]
- [tex]\( D^{\prime \prime}(0, -1) \)[/tex]
This matches the target vertices. Therefore, Option 1 is the correct transformation sequence.
Given the correct transformation, we do not need to check the rest. But for completeness:
### Option 2: [tex]\((x, y) \rightarrow (-x, y) \rightarrow (x+1, y+1)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (-x, y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(-2, -1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(1, 2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+1, y+1)\)[/tex]
- [tex]\( B'(3, 0) \rightarrow B^{\prime \prime}(4, 1) \)[/tex]
- [tex]\( C'(-2, -1) \rightarrow C^{\prime \prime}(-1, 0) \)[/tex]
- [tex]\( D'(1, 2) \rightarrow D^{\prime \prime}(2, 3) \)[/tex]
These vertices do not match the target vertices.
### Option 3: [tex]\((x, y) \rightarrow (x, -y) \rightarrow (x+2, y+2)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (x, -y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(-3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(2, 1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(-1, -2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+2, y+2)\)[/tex]
- [tex]\( B'(-3, 0) \rightarrow B^{\prime \prime}(-1, 2) \)[/tex]
- [tex]\( C'(2, 1) \rightarrow C^{\prime \prime}(4, 3) \)[/tex]
- [tex]\( D'(-1, -2) \rightarrow D^{\prime \prime}(1, 0) \)[/tex]
These vertices do not match the target vertices.
### Option 4: [tex]\((x, y) \rightarrow (-x, y) \rightarrow (x+2, y+2)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (-x, y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(-2, -1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(1, 2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+2, y+2)\)[/tex]
- [tex]\( B'(3, 0) \rightarrow B^{\prime \prime}(5, 2) \)[/tex]
- [tex]\( C'(-2, -1) \rightarrow C^{\prime \prime}(0, 1) \)[/tex]
- [tex]\( D'(1, 2) \rightarrow D^{\prime \prime}(3, 4) \)[/tex]
These vertices do not match the target vertices.
Therefore, the correct sequence of transformations to achieve the desired vertices is:
Option 1: [tex]\((x, y) \rightarrow (x, -y) \rightarrow (x+1, y+1)\)[/tex]
Let's check the options provided step by step.
### Option 1: [tex]\((x, y) \rightarrow (x, -y) \rightarrow (x+1, y+1)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (x, -y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(-3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(2, 1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(-1, -2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+1, y+1)\)[/tex]
- [tex]\( B'(-3, 0) \rightarrow B^{\prime \prime}(-2, 1) \)[/tex]
- [tex]\( C'(2, 1) \rightarrow C^{\prime \prime}(3, 2) \)[/tex]
- [tex]\( D'(-1, -2) \rightarrow D^{\prime \prime}(0, -1) \)[/tex]
As a result, we obtain the vertices:
- [tex]\( B^{\prime \prime}(-2, 1) \)[/tex]
- [tex]\( C^{\prime \prime}(3, 2) \)[/tex]
- [tex]\( D^{\prime \prime}(0, -1) \)[/tex]
This matches the target vertices. Therefore, Option 1 is the correct transformation sequence.
Given the correct transformation, we do not need to check the rest. But for completeness:
### Option 2: [tex]\((x, y) \rightarrow (-x, y) \rightarrow (x+1, y+1)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (-x, y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(-2, -1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(1, 2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+1, y+1)\)[/tex]
- [tex]\( B'(3, 0) \rightarrow B^{\prime \prime}(4, 1) \)[/tex]
- [tex]\( C'(-2, -1) \rightarrow C^{\prime \prime}(-1, 0) \)[/tex]
- [tex]\( D'(1, 2) \rightarrow D^{\prime \prime}(2, 3) \)[/tex]
These vertices do not match the target vertices.
### Option 3: [tex]\((x, y) \rightarrow (x, -y) \rightarrow (x+2, y+2)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (x, -y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(-3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(2, 1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(-1, -2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+2, y+2)\)[/tex]
- [tex]\( B'(-3, 0) \rightarrow B^{\prime \prime}(-1, 2) \)[/tex]
- [tex]\( C'(2, 1) \rightarrow C^{\prime \prime}(4, 3) \)[/tex]
- [tex]\( D'(-1, -2) \rightarrow D^{\prime \prime}(1, 0) \)[/tex]
These vertices do not match the target vertices.
### Option 4: [tex]\((x, y) \rightarrow (-x, y) \rightarrow (x+2, y+2)\)[/tex]
First Transformation: [tex]\((x, y) \rightarrow (-x, y)\)[/tex]
- [tex]\( B(-3, 0) \rightarrow B'(3, 0) \)[/tex]
- [tex]\( C(2, -1) \rightarrow C'(-2, -1) \)[/tex]
- [tex]\( D(-1, 2) \rightarrow D'(1, 2) \)[/tex]
Second Transformation: [tex]\((x, y) \rightarrow (x+2, y+2)\)[/tex]
- [tex]\( B'(3, 0) \rightarrow B^{\prime \prime}(5, 2) \)[/tex]
- [tex]\( C'(-2, -1) \rightarrow C^{\prime \prime}(0, 1) \)[/tex]
- [tex]\( D'(1, 2) \rightarrow D^{\prime \prime}(3, 4) \)[/tex]
These vertices do not match the target vertices.
Therefore, the correct sequence of transformations to achieve the desired vertices is:
Option 1: [tex]\((x, y) \rightarrow (x, -y) \rightarrow (x+1, y+1)\)[/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
