question 1 of 10
which of the following steps were applied to $\delta abc$ to obtain $\delta abc$?
a. shifted 4 units left and 2 units down
b. shifted 3 units left and 2 units down
c. shifted 4 units left and 3 units down
d. shifted 3 units left and 3 units down

Question

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": [ "Linear Transformations" ], "new_concepts": [ "Geometric Translations", "Coordinate Shifts" ], "current_concepts": [ "Linear Transformations", "Geometric Translations", "Coordinate Shifts" ] } ## Identify coordinates of original vertices Using the *Linear Transformations* knowledge point $$ A = (3, 6),\quad B = (5, 9),\quad C = (7, 6) $$ ## Identify coordinates of image vertices Using the *Linear Transformations* knowledge point $$ A' = (-1, 3),\quad B' = (1, 6),\quad C' = (3, 3) $$ ## Calculate horizontal and vertical shifts Using the *Linear Transformations* knowledge point $$ \begin{aligned} \Delta x &= x_{A'} - x_A = -1 - 3 = -4\ \Delta y &= y_{A'} - y_A = 3 - 6 = -3 \end{aligned} $$ ## Interpret the shift direction and magnitude Using the *Linear Transformations* knowledge point $$ \begin{aligned} &\Delta x = -4 \implies \text{Shifted 4 units left}\ &\Delta y = -3 \implies \text{Shifted 3 units down} \end{aligned} $$

A. Shifted 4 units left and 2 units down

B. Shifted 3 units left and 2 units down

C. Shifted 4 units left and 3 units down

D. Shifted 3 units left and 3 units down

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

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Question

Explanation:

Identify coordinates of original vertices

Identify coordinates of image vertices

Calculate horizontal and vertical shifts

Interpret the shift direction and magnitude

Answer: