triangle def has coordinates $d(-3, -2)$, $e(-1, -2)$, $f(-2, -4)$.
the triangle is translated so its image has coordinates $d(1, -4)$, $e(3, -4)$, $f(2, -6)$.

which statement shows the rule for the translation?
$(x, y) \
ightarrow (x - 4, y - 2)$
$(x, y) \
ightarrow (x - 4, y + 2)$
$(x, y) \
ightarrow (x + 4, y + 2)$
$(x, y) \
ightarrow (x + 4, y - 2)$

Question

triangle def has coordinates $d(-3, -2)$, $e(-1, -2)$, $f(-2, -4)$.
the triangle is translated so its image has coordinates $d(1, -4)$, $e(3, -4)$, $f(2, -6)$.

which statement shows the rule for the translation?
$(x, y) \
ightarrow (x - 4, y - 2)$
$(x, y) \
ightarrow (x - 4, y + 2)$
$(x, y) \
ightarrow (x + 4, y + 2)$
$(x, y) \
ightarrow (x + 4, y - 2)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Coordinate Translation", "Translation Rule" ], "current_concepts": [ "Coordinate Translation", "Translation Rule", "Geometric Transformations" ] } ## Determine the horizontal shift $$ \begin{aligned} x' &= x + a \ 1 &= -3 + a \ a &= 4 \end{aligned} $$ ## Determine the vertical shift $$ \begin{aligned} y' &= y + b \ -4 &= -2 + b \ b &= -2 \end{aligned} $$ ## Formulate the translation rule $$ (x, y) ightarrow (x + 4, y - 2) $$

(A) $(x, y) ightarrow (x - 4, y - 2)$

(B) $(x, y) ightarrow (x - 4, y + 2)$

(C) $(x, y) ightarrow (x + 4, y + 2)$

(D) $(x, y) ightarrow (x + 4, y - 2)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Translation" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the horizontal shift

Determine the vertical shift

Formulate the translation rule

Answer: