Question

Math

Posted 4 months ago

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Anju tried to define a reflection.
- For any point $R$ on the line of reflection $\ell$, the image $R^{\prime}$ is at the same point as $R$.
- For any point $P$ not on the line of reflection $\ell$, the image $P^{\prime}$ is on the other side of $\ell$ such that $\overline{P P^{\prime}}$ is perpendicular to $\ell$.
What mistake did Anju make in her definition of a reflection?
Choose 1 answer:
(A) $\overline{P P^{\prime}}$ must be parallel to the line of reflection, not perpendicular.
(B) Points $P$ and $P^{\prime}$ must be the same distance from the line of reflection.
(C) Anju needed to include the direction of the reflection.
(D) Anju did not make a mistake.
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 2

Identify the mistake in Anju's definition based on the properties of a reflection

step 3

A reflection across line $\ell$ means that for any point $P$ not on $\ell$, the line segment $\overline{P P^{\prime}}$ is perpendicular to $\ell$ and bisected by $\ell$

step 4

Anju's definition incorrectly states the relationship between $\overline{P P^{\prime}}$ and $\ell$

step 5

The correct property is that points $P$ and $P^{\prime}$ must be equidistant from the line of reflection $\ell$

1 Answer

B

Key Concept

Reflection in Geometry

Explanation

In a reflection, every point and its image are equidistant from the line of reflection, and the line connecting a point and its image is perpendicular to the line of reflection.

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