question 9 of 10

abcd is rotated counterclockwise about the origin. by how many degrees was abcd rotated?

a. 90°
b. 270°
c. 180°
d. 360°

Question

question 9 of 10

abcd is rotated counterclockwise about the origin. by how many degrees was abcd rotated?

a. 90°
b. 270°
c. 180°
d. 360°

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 coordinates of original and rotated vertices Using the *Coordinate Geometry Transformations* knowledge point $$ \begin{aligned} &A = (3, 3), \quad B = (3, 7), \quad C = (7, 7), \quad D = (7, 3)\ &A' = (-3, -3), \quad B' = (-3, -7), \quad C' = (-7, -7), \quad D' = (-7, -3) \end{aligned} $$ ## Determine the rotation angle Using the *Geometric Rotations* knowledge point $$ \begin{aligned} &(x, y) \to (-x, -y)\ &\theta = 180^\circ \end{aligned} $$

A. $90^\circ$

B. $270^\circ$

C. $180^\circ$

D. $360^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of original and rotated vertices

Determine the rotation angle

Answer: