the rule $r_{y-\text{axis}} \circ r_{o, 90^{\circ}}(x, y)$ is applied to $\delta abc$.

which triangle shows the final image?

1
2
3
4

Question

the rule $r_{y-\text{axis}} \circ r_{o, 90^{\circ}}(x, y)$ is applied to $\delta abc$.

which triangle shows the final image?

1
2
3
4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Composition of Transformations", "Geometric Rotations", "Geometric Reflections" ], "new_concepts": [], "current_concepts": [ "Composition of Transformations", "Geometric Rotations", "Geometric Reflections" ] } ## Identify the vertices of the original triangle Using the *Composition of Transformations* knowledge point $$ \begin{aligned} A &= (2, -4) \ B &= (4, -4) \ C &= (4, -2) \end{aligned} $$ ## Apply the rotation transformation Using the *Geometric Rotations* knowledge point $$ \begin{aligned} R_{O, 90^\circ}(x, y) &= (-y, x) \ A' &= (4, 2) \ B' &= (4, 4) \ C' &= (2, 4) \end{aligned} $$ ## Apply the reflection transformation Using the *Geometric Reflections* knowledge point $$ \begin{aligned} r_{y\text{-axis}}(x, y) &= (-x, y) \ A'' &= (-4, 2) \ B'' &= (-4, 4) \ C'' &= (-2, 4) \end{aligned} $$ ## Match the final coordinates to the numbered triangles Using the *Composition of Transformations* knowledge point $$ \begin{aligned} &\text{Vertices of Triangle 1: } (-4, 2), (-4, 4), (-3, 3) \quad (\text{Incorrect}) \ &\text{Vertices of Triangle 2: } (-4, 2), (-4, 4), (-2, 4) \quad (\text{Correct}) \end{aligned} $$

1

2

3

4

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Composition of Transformations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the vertices of the original triangle

Apply the rotation transformation

Apply the reflection transformation

Match the final coordinates to the numbered triangles

Answer: