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.

Question

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.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Review Anju's definition of a reflection and the properties of a reflection. ‖ ‖ 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.⚹◊What is the correct relationship between the points $P, P^{'}$, and the line of reflection $l$ in a reflection transformation?⍭ Generate me a similar question◊

Sia