Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

A point has the coordinates [tex]\((m, 0)\)[/tex] where [tex]\(m \neq 0\)[/tex].

Which reflection of the point will produce an image located at [tex]\((0, -m)\)[/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
Let's analyze the reflections for the point [tex]\( (m, 0) \)[/tex] where [tex]\( m \neq 0 \)[/tex].

1. Reflection across the [tex]\( x \)[/tex]-axis:
- When you reflect a point [tex]\( (x, y) \)[/tex] across the [tex]\( x \)[/tex]-axis, the [tex]\( y \)[/tex]-coordinate changes sign, while the [tex]\( x \)[/tex]-coordinate remains the same.
- Thus, reflecting [tex]\( (m, 0) \)[/tex] across the [tex]\( x \)[/tex]-axis yields [tex]\( (m, -0) = (m, 0) \)[/tex].

2. Reflection across the [tex]\( y \)[/tex]-axis:
- When you reflect a point [tex]\( (x, y) \)[/tex] across the [tex]\( y \)[/tex]-axis, the [tex]\( x \)[/tex]-coordinate changes sign, while the [tex]\( y \)[/tex]-coordinate remains the same.
- Thus, reflecting [tex]\( (m, 0) \)[/tex] across the [tex]\( y \)[/tex]-axis yields [tex]\( (-m, 0) \)[/tex].

3. Reflection across the line [tex]\( y = x \)[/tex]:
- When you reflect a point [tex]\( (x, y) \)[/tex] across the line [tex]\( y = x \)[/tex], the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] coordinates swap.
- Thus, reflecting [tex]\( (m, 0) \)[/tex] across the line [tex]\( y = x \)[/tex] yields [tex]\( (0, m) \)[/tex].

4. Reflection across the line [tex]\( y = -x \)[/tex]:
- When you reflect a point [tex]\( (x, y) \)[/tex] across the line [tex]\( y = -x \)[/tex], the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] coordinates swap and both change signs.
- Thus, reflecting [tex]\( (m, 0) \)[/tex] across the line [tex]\( y = -x \)[/tex] yields [tex]\( (0, -m) \)[/tex].

To determine the location of the image point [tex]\( (0, -m) \)[/tex], we can see from the analysis above that it is obtained by reflecting the original point [tex]\( (m, 0) \)[/tex] across the line [tex]\( y = -x \)[/tex].

Therefore, the correct reflection is across the line [tex]\( y = -x \)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.