Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our 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].
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.