Answered

Get the information you need with the help of IDNLearn.com's extensive Q&A platform. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

Given the ordered pair [tex]\((1, -3)\)[/tex], where will the transformed image be after the following composition: [tex]\(D_2 \circ R_{y-axis}\)[/tex]?

Sagot :

GinnyAnsweridn
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].
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.