the image of trapezoid pqrs after a reflection across $\overleftrightarrow{wy}$ is trapezoid pqrs.

what is the relationship between $\overline{rr}$ and $\overline{ss}$?

$rr = 2ss$
$rr = 4ss$
$\overline{rr} \parallel \overline{ss}$
$\overline{rr} \perp \overline{ss}$

Question

the image of trapezoid pqrs after a reflection across $\overleftrightarrow{wy}$ is trapezoid pqrs.

what is the relationship between $\overline{rr}$ and $\overline{ss}$?

$rr = 2ss$
$rr = 4ss$
$\overline{rr} \parallel \overline{ss}$
$\overline{rr} \perp \overline{ss}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Reflection Rules" ], "new_concepts": [ "Geometric Reflections", "Properties of Reflections" ], "current_concepts": [ "Reflection Rules", "Geometric Reflections", "Properties of Reflections" ] } ## Identify properties of geometric reflections $$ \begin{aligned} &\text{Let } \overleftrightarrow{WY} \text{ be the line of reflection.}\ &\text{By definition of reflection, the segment connecting a point to its image is perpendicular to the line of reflection:}\ &\overline{RR'} \perp \overleftrightarrow{WY} \quad \text{and} \quad \overline{SS'} \perp \overleftrightarrow{WY} \end{aligned} $$ ## Determine the relationship between the segments $$ \begin{aligned} &\text{Since both segments } \overline{RR'} \text{ and } \overline{SS'} \text{ are perpendicular to the same line } \overleftrightarrow{WY}\text{:}\ &\overline{RR'} \parallel \overline{SS'} \end{aligned} $$

(A) $RR' = 2SS'$

(B) $RR' = 4SS'$ (C) $\overline{RR'} \parallel \overline{SS'}$

(D) $\overline{RR'} \perp \overline{SS'}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Geometric Reflections" ] }

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QUESTION IMAGE

Question

Explanation:

Identify properties of geometric reflections

Determine the relationship between the segments

Answer: