Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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 what happens to the point under each type of reflection.

1. Reflection across the x-axis:
- Reflecting a point [tex]\((x, y)\)[/tex] across the x-axis results in the point [tex]\((x, -y)\)[/tex].
- For [tex]\((0, k)\)[/tex], the point becomes [tex]\((0, -k)\)[/tex] after reflection.

2. Reflection across the y-axis:
- Reflecting a point [tex]\((x, y)\)[/tex] across the y-axis results in the point [tex]\((-x, y)\)[/tex].
- For [tex]\((0, k)\)[/tex], the point remains [tex]\((0, k)\)[/tex] after reflection.

3. Reflection across the line [tex]\(y = x\)[/tex]:
- Reflecting a point [tex]\((x, y)\)[/tex] across the line [tex]\(y = x\)[/tex] results in the point [tex]\((y, x)\)[/tex].
- For [tex]\((0, k)\)[/tex], the point becomes [tex]\((k, 0)\)[/tex] after reflection.

4. Reflection across the line [tex]\(y = -x\)[/tex]:
- Reflecting a point [tex]\((x, y)\)[/tex] across the line [tex]\(y = -x\)[/tex] results in the point [tex]\((-y, -x)\)[/tex].
- For [tex]\((0, k)\)[/tex], the point becomes [tex]\((-k, 0)\)[/tex] after reflection.

Now, among all these reflections, only the reflection across the y-axis keeps the point’s coordinates the same, which means that the point [tex]\((0, k)\)[/tex] remains [tex]\((0, k)\)[/tex].

Therefore, the correct answer is:
- A reflection of the point across the y-axis will produce an image at the same coordinates [tex]\((0, k)\)[/tex].
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.