in which quadrant does the point $(4, -3)$ lie?

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

Question

in which quadrant does the point $(4, -3)$ 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" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Cartesian Coordinate System", "Quadrants" ], "current_concepts": [ "Cartesian Coordinate System", "Quadrants" ] } ## Identify the coordinates of the point The given point is $(4, -3)$. Here, the x-coordinate is $x = 4$ and the y-coordinate is $y = -3$. ## Analyze the signs of the coordinates The x-coordinate is positive ($x > 0$) and the y-coordinate is negative ($y < 0$). ## Determine the corresponding quadrant In the Cartesian plane, the four quadrants are defined by the signs of the coordinates: - Quadrant I: $x > 0, y > 0$ - Quadrant II: $x < 0, y > 0$ - Quadrant III: $x < 0, y < 0$ - Quadrant IV: $x > 0, y < 0$ Since $x = 4$ (positive) and $y = -3$ (negative), the point lies in Quadrant IV.

I

II

III

IV

{ "elements": [ { "type": "point", "params": [[4, -3]], "properties": { "name": "(4, -3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "text", "params": [5, 5, "Quadrant I"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [-5, 5, "Quadrant II"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [-5, -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", "Cartesian Coordinate System" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the point

Analyze the signs of the coordinates

Determine the corresponding quadrant

Answer: