oliviarubinstein0
Answered

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A point has the coordinates (0, k).
Which reflection of the point will produce an image at the same coordinates, (0, k)?
Oa reflection of the point across the x-axis
OOOO
a reflection of the point across the y-axis
a reflection of the point across the line y = x
a reflection of the point across the line y=-x

Sagot :

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

1. Reflection across the x-axis:
- For any point [tex]\((x, y)\)[/tex], reflecting it across the x-axis results in the new point [tex]\((x, -y)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflection across the x-axis yields [tex]\((0, -k)\)[/tex].

2. Reflection across the y-axis:
- For any point [tex]\((x, y)\)[/tex], reflecting it across the y-axis results in the new point [tex]\((-x, y)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflection across the y-axis yields [tex]\((0, k)\)[/tex].

3. Reflection across the line [tex]\(y = x\)[/tex]:
- For any point [tex]\((x, y)\)[/tex], reflecting it across the line [tex]\(y = x\)[/tex] results in the new point [tex]\((y, x)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflection across the line [tex]\(y = x\)[/tex] yields [tex]\((k, 0)\)[/tex].

4. Reflection across the line [tex]\(y = -x\)[/tex]:
- For any point [tex]\((x, y)\)[/tex], reflecting it across the line [tex]\(y = -x\)[/tex] results in the new point [tex]\((-y, -x)\)[/tex].
- For the point [tex]\((0, k)\)[/tex], reflection across the line [tex]\(y = -x\)[/tex] yields [tex]\((-k, 0)\)[/tex].

Of all these transformations, only the reflection across the y-axis results in the point retaining its original coordinates [tex]\((0, k)\)[/tex].

Therefore, the correct answer is:
- a reflection of the point across the y-axis
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