question 10 (1 point)

a quadrilateral is drawn on the coordinate plane with the following coordinates: a(0, 0), b(5, 5), c(6, 12), and d(1, 7).

which of the following is this quadrilateral?

rhombus
square
parallelogram
rectangle

Question

question 10 (1 point)

a quadrilateral is drawn on the coordinate plane with the following coordinates: a(0, 0), b(5, 5), c(6, 12), and d(1, 7).

which of the following is this quadrilateral?

rhombus
square
parallelogram
rectangle

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 $$ \begin{aligned} &AB = \sqrt{(5-0)^2 + (5-0)^2} = \sqrt{25+25} = \sqrt{50} = 5\sqrt{2}\ &BC = \sqrt{(6-5)^2 + (12-5)^2} = \sqrt{1+49} = \sqrt{50} = 5\sqrt{2}\ &CD = \sqrt{(1-6)^2 + (7-12)^2} = \sqrt{25+25} = \sqrt{50} = 5\sqrt{2}\ &DA = \sqrt{(0-1)^2 + (0-7)^2} = \sqrt{1+49} = \sqrt{50} = 5\sqrt{2} \end{aligned} $$ ## Calculate gradients of adjacent sides $$ \begin{aligned} &m_{AB} = \frac{5-0}{5-0} = 1\ &m_{BC} = \frac{12-5}{6-5} = 7\ &m_{AB} \cdot m_{BC} = 1 \cdot 7 = 7 eq -1 \end{aligned} $$ ## Classify the quadrilateral $$ \begin{aligned} &AB = BC = CD = DA = 5\sqrt{2} \implies \text{Rhombus}\ &m_{AB} \cdot m_{BC} eq -1 \implies \text{Not a square} \end{aligned} $$

rhombus

square

parallelogram

rectangle

{ "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "A(0,0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, 5]], "properties": { "name": "B(5,5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, 12]], "properties": { "name": "C(6,12)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 7]], "properties": { "name": "D(1,7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "polygon", "params": [[0, 0], [5, 5], [6, 12], [1, 7]], "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 gradients of adjacent sides

Classify the quadrilateral

Answer: