question 6 (1 point)

a quadrilateral is drawn on the coordinate plane with the following coordinates: a (0) b (3, 4), c (-1, 7), and d (-4, 3).

which of the following is this quadrilateral?

rectangle
rhombus
square
parallelogram

Question

question 6 (1 point)

a quadrilateral is drawn on the coordinate plane with the following coordinates: a (0) b (3, 4), c (-1, 7), and d (-4, 3).

which of the following is this quadrilateral?

rectangle
rhombus
square
parallelogram

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Coordinate Geometry", "Gradient Formula", "Distance Formula", "Quadrilateral Classification" ], "new_concepts": [], "current_concepts": [ "Coordinate Geometry", "Gradient Formula", "Distance Formula", "Quadrilateral Classification" ] } ## Calculate side lengths $$ \begin{aligned} &A(0, 0),\ B(3, 4),\ C(-1, 7),\ D(-4, 3)\ &AB = \sqrt{(3-0)^2 + (4-0)^2} = \sqrt{9+16} = 5\ &BC = \sqrt{(-1-3)^2 + (7-4)^2} = \sqrt{16+9} = 5\ &CD = \sqrt{(-4-(-1))^2 + (3-7)^2} = \sqrt{9+16} = 5\ &DA = \sqrt{(0-(-4))^2 + (0-3)^2} = \sqrt{16+9} = 5 \end{aligned} $$ ## Calculate diagonal lengths $$ \begin{aligned} &AC = \sqrt{(-1-0)^2 + (7-0)^2} = \sqrt{1+49} = \sqrt{50} = 5\sqrt{2}\ &BD = \sqrt{(-4-3)^2 + (3-4)^2} = \sqrt{49+1} = \sqrt{50} = 5\sqrt{2} \end{aligned} $$ ## Classify the quadrilateral $$ \begin{aligned} &AB = BC = CD = DA = 5 \implies \text{Rhombus}\ &AC = BD = 5\sqrt{2} \implies \text{Square} \end{aligned} $$

rectangle

rhombus

square

parallelogram

{ "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "A(0,0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[3, 4]], "properties": { "name": "B(3,4)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-1, 7]], "properties": { "name": "C(-1,7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-4, 3]], "properties": { "name": "D(-4,3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "polygon", "params": [[0, 0], [3, 4], [-1, 7], [-4, 3]], "properties": { "fillColor": "rgba(140, 85, 242, 0.15)", "strokeColor": "#8C55F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Quadrilateral Classification" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate side lengths

Calculate diagonal lengths

Classify the quadrilateral

Answer: