question 6 of 25

how many degrees has $\delta abc$ been rotated counterclockwise about the origin?

a. $270^\circ$
b. $360^\circ$
c. $180^\circ$
d. $90^\circ$

Question

question 6 of 25

how many degrees has $\delta abc$ been rotated counterclockwise about the origin?

a. $270^\circ$
b. $360^\circ$
c. $180^\circ$
d. $90^\circ$

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": [ "Geometric Rotations", "Coordinate Geometry Transformations" ], "new_concepts": [], "current_concepts": [ "Geometric Rotations", "Coordinate Geometry Transformations" ] } ## Identify the coordinates of the original vertices Using the **Coordinate Geometry Transformations** knowledge point $$ \begin{aligned} A &= (-5, 3) \ B &= (-3, 6) \ C &= (-1, 4) \end{aligned} $$ ## Identify the coordinates of the rotated vertices Using the **Coordinate Geometry Transformations** knowledge point $$ \begin{aligned} A' &= (-3, -5) \ B' &= (-6, -3) \ C' &= (-4, -1) \end{aligned} $$ ## Determine the transformation rule Using the **Geometric Rotations** knowledge point $$ (x, y) \to (y, -x) $$ ## Find the angle of rotation Using the **Geometric Rotations** knowledge point $$ \begin{aligned} R_{90^\circ}(x, y) &= (-y, x) \ R_{180^\circ}(x, y) &= (-x, -y) \ R_{270^\circ}(x, y) &= (y, -x) \end{aligned} $$ Thus, the counterclockwise rotation about the origin is $270^\circ$.

A. $270^\circ$

B. $360^\circ$

C. $180^\circ$

D. $90^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the original vertices

Identify the coordinates of the rotated vertices

Determine the transformation rule

Find the angle of rotation

Answer: