jean transformed a point by using the rule $(x, y) \
ightarrow (x - 6, y + 8)$. the image point is $(-4, 1)$. which point is the pre-image?

$(-10, 9)$
$(2, -7)$
$(-2, 7)$
$(10, -9)$

Question

jean transformed a point by using the rule $(x, y) \
ightarrow (x - 6, y + 8)$. the image point is $(-4, 1)$. which point is the pre-image?

$(-10, 9)$
$(2, -7)$
$(-2, 7)$
$(10, -9)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Translation Rule", "Coordinate Transformations" ], "new_concepts": [], "current_concepts": [ "Translation Rule", "Coordinate Transformations" ] } ## Set up the transformation equations Using the **Translation Rule** and **Coordinate Transformations** knowledge points $$ \begin{aligned} &x - 6 = -4 \ &y + 8 = 1 \end{aligned} $$ ## Solve for the pre-image coordinates Using the **Coordinate Transformations** knowledge point $$ \begin{aligned} &x = -4 + 6 = 2 \ &y = 1 - 8 = -7 \end{aligned} $$

(A) $(-10, 9)$

(B) $(2, -7)$

(C) $(-2, 7)$

(D) $(10, -9)$

{ "elements": [ { "type": "point", "params": [[2, -7]], "properties": { "name": "Pre-image (2, -7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-4, 1]], "properties": { "name": "Image (-4, 1)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "arrow", "params": [[2, -7], [-4, 1]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the transformation equations

Solve for the pre-image coordinates

Answer: