Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Certainly! Let's transform the given ordered pair [tex]\((1, -3)\)[/tex] through the described transformations step-by-step.
### Step 1: Reflection over the y-axis
To reflect a point over the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same:
- Original Point: [tex]\((1, -3)\)[/tex]
- Reflected Point: [tex]\((-1, -3)\)[/tex]
### Step 2: Scaling by a factor of 2
Next, we scale the reflected coordinates by a factor of 2. This means we multiply both the x and y coordinates by 2:
- Reflected Point: [tex]\((-1, -3)\)[/tex]
- Transformed Point: [tex]\((-2 \cdot (-1), 2 \cdot (-3))\)[/tex]
So, after we multiply:
- Transformed Coordinates: [tex]\((-2, -6)\)[/tex]
### Summary
1. Reflection over the y-axis:
- From [tex]\((1, -3)\)[/tex] to [tex]\((-1, -3)\)[/tex]
2. Scaling by a factor of 2:
- From [tex]\((-1, -3)\)[/tex] to [tex]\((-2, -6)\)[/tex]
Therefore, the final transformed image of the original point [tex]\((1, -3)\)[/tex] through the composition [tex]\(D_2 \circ R_{\text{y-axis}}\)[/tex] will be:
[tex]\[ (-2, -6) \][/tex]
Additionally, the intermediate reflected coordinates are [tex]\((-1, -3)\)[/tex].
### Step 1: Reflection over the y-axis
To reflect a point over the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same:
- Original Point: [tex]\((1, -3)\)[/tex]
- Reflected Point: [tex]\((-1, -3)\)[/tex]
### Step 2: Scaling by a factor of 2
Next, we scale the reflected coordinates by a factor of 2. This means we multiply both the x and y coordinates by 2:
- Reflected Point: [tex]\((-1, -3)\)[/tex]
- Transformed Point: [tex]\((-2 \cdot (-1), 2 \cdot (-3))\)[/tex]
So, after we multiply:
- Transformed Coordinates: [tex]\((-2, -6)\)[/tex]
### Summary
1. Reflection over the y-axis:
- From [tex]\((1, -3)\)[/tex] to [tex]\((-1, -3)\)[/tex]
2. Scaling by a factor of 2:
- From [tex]\((-1, -3)\)[/tex] to [tex]\((-2, -6)\)[/tex]
Therefore, the final transformed image of the original point [tex]\((1, -3)\)[/tex] through the composition [tex]\(D_2 \circ R_{\text{y-axis}}\)[/tex] will be:
[tex]\[ (-2, -6) \][/tex]
Additionally, the intermediate reflected coordinates are [tex]\((-1, -3)\)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.