Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

A point has the coordinates [tex]$(0, k)$[/tex].

Which reflection of the point will produce an image at the same coordinates, [tex]$(0, k)$[/tex]?

A. a reflection of the point across the [tex]$x$[/tex]-axis
B. a reflection of the point across the [tex]$y$[/tex]-axis
C. a reflection of the point across the line [tex]$y=x$[/tex]
D. a reflection of the point across the line [tex]$y=-x$[/tex]

Sagot :

GinnyAnswer
To determine which reflection of the point [tex]\((0, k)\)[/tex] will produce an image at the same coordinates [tex]\((0, k)\)[/tex], let's analyze each possible reflection:

1. Reflection across the [tex]\(x\)[/tex]-axis:
- The reflection of a point [tex]\((x, y)\)[/tex] across the [tex]\(x\)[/tex]-axis changes its coordinates to [tex]\((x, -y)\)[/tex].
- If we reflect the point [tex]\((0, k)\)[/tex] across the [tex]\(x\)[/tex]-axis, it becomes [tex]\((0, -k)\)[/tex].

2. Reflection across the [tex]\(y\)[/tex]-axis:
- The reflection of a point [tex]\((x, y)\)[/tex] across the [tex]\(y\)[/tex]-axis changes its coordinates to [tex]\((-x, y)\)[/tex].
- If we reflect the point [tex]\((0, k)\)[/tex] across the [tex]\(y\)[/tex]-axis, it becomes [tex]\((0, k)\)[/tex].

3. Reflection across the line [tex]\(y=x\)[/tex]:
- The reflection of a point [tex]\((x, y)\)[/tex] across the line [tex]\(y=x\)[/tex] changes its coordinates to [tex]\((y, x)\)[/tex].
- If we reflect the point [tex]\((0, k)\)[/tex] across the line [tex]\(y=x\)[/tex], it becomes [tex]\((k, 0)\)[/tex].

4. Reflection across the line [tex]\(y=-x\)[/tex]:
- The reflection of a point [tex]\((x, y)\)[/tex] across the line [tex]\(y=-x\)[/tex] changes its coordinates to [tex]\((-y, -x)\)[/tex].
- If we reflect the point [tex]\((0, k)\)[/tex] across the line [tex]\(y=-x\)[/tex], it becomes [tex]\((-k, 0)\)[/tex].

From the above analysis, we see that among all the reflections, only the reflection across the [tex]\(x\)[/tex]-axis keeps the coordinates of the point [tex]\((0, k)\)[/tex] unchanged.

Therefore, the correct answer is:
- a reflection of the point across the [tex]\(x\)[/tex]-axis
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.