in which quadrant does the point $(-2, -6)$ lie?

$\bigcirc$ i
$\bigcirc$ ii
$\bigcirc$ iii
$\bigcirc$ iv

Question

in which quadrant does the point $(-2, -6)$ lie?

$\bigcirc$ i
$\bigcirc$ ii
$\bigcirc$ iii
$\bigcirc$ iv

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": [ "Cartesian Coordinate System", "Quadrants" ], "new_concepts": [], "current_concepts": [ "Cartesian Coordinate System", "Quadrants" ] } ## Identify the coordinates of the point Using the *Cartesian Coordinate System* knowledge point $$ (x, y) = (-2, -6) $$ ## Determine the signs of the coordinates Using the *Cartesian Coordinate System* knowledge point $$ \begin{aligned} x &= -2 < 0 \ y &= -6 < 0 \end{aligned} $$ ## Determine the quadrant Using the *Quadrants* knowledge point $$ \begin{aligned} &\text{Quadrant I: } x > 0, y > 0 \ &\text{Quadrant II: } x < 0, y > 0 \ &\text{Quadrant III: } x < 0, y < 0 \ &\text{Quadrant IV: } x > 0, y < 0 \end{aligned} $$ Since both coordinates are negative, the point lies in Quadrant III.

I

II

III

IV

{ "elements": [ { "type": "point", "params": [[-2, -6]], "properties": { "name": "(-2, -6)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "text", "params": [5, 5, "Quadrant I"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [-7, 5, "Quadrant II"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [-7, -5, "Quadrant III"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [5, -5, "Quadrant IV"], "properties": { "color": "#583C87" } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Quadrants" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the point

Determine the signs of the coordinates

Determine the quadrant

Answer: