Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A 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 will produce an image of the point [tex]\((0, k)\)[/tex] at the same coordinates [tex]\((0, k)\)[/tex], we need to examine how each type of reflection affects the coordinates of the point.

1. Reflection across the [tex]$x$[/tex]-axis:
- The reflection of a point [tex]\((x, y)\)[/tex] across the [tex]$x$[/tex]-axis is [tex]\((x, -y)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflecting across the [tex]$x$[/tex]-axis gives us the point [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 is [tex]\((-x, y)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflecting across the [tex]$y$[/tex]-axis gives us the point [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] is [tex]\((y, x)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflecting across the line [tex]$y = x$[/tex] gives us the point [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] is [tex]\((-y, -x)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflecting across the line [tex]$y = -x$[/tex] gives us the point [tex]\((-k, 0)\)[/tex].

From the analysis above, it is clear that reflecting the point [tex]\((0, k)\)[/tex] across the [tex]$y$[/tex]-axis will produce an image at the same coordinates [tex]\((0, k)\)[/tex]. Therefore, the correct reflection type is:

A reflection of the point across the [tex]$y$[/tex]-axis.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.