avaprincessbra22
Answered

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The point [tex]\((-7,1)\)[/tex] when reflected across the origin maps onto:

A) [tex]\((7,-1)\)[/tex]

B) [tex]\((1,-7)\)[/tex]

C) [tex]\((7,1)\)[/tex]

D) [tex]\((-1,7)\)[/tex]

Sagot :

GinnyAnswer
To determine the reflection of the point [tex]\((-7, 1)\)[/tex] across the origin, follow these steps:

1. Understand Reflection Across the Origin:
When a point [tex]\((x, y)\)[/tex] is reflected across the origin, its coordinates are transformed to [tex]\((-x, -y)\)[/tex]. This means both the [tex]\(x\)[/tex]-coordinate and the [tex]\(y\)[/tex]-coordinate change their signs.

2. Apply the Transformation:
- For the point [tex]\((-7, 1)\)[/tex]:
- The [tex]\(x\)[/tex]-coordinate is [tex]\(-7\)[/tex]. When reflected across the origin, it becomes [tex]\(-(-7)\)[/tex] which is [tex]\(7\)[/tex].
- The [tex]\(y\)[/tex]-coordinate is [tex]\(1\)[/tex]. When reflected across the origin, it becomes [tex]\(-(1)\)[/tex] which is [tex]\(-1\)[/tex].

3. Combine the Transformed Coordinates:
Therefore, the point [tex]\((-7, 1)\)[/tex] when reflected across the origin, maps onto [tex]\((7, -1)\)[/tex].

Thus, the correct answer is:

A) [tex]\((7, -1)\)[/tex]
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