find the perimeter of a quadrilateral with vertices at c (2, 4), d (1, 1), e (5, 0), and f (3, 4). round your answer to the nearest hundredth when necessary.

12.76 units
16.25 units
20.12 units
24.85 units

Question

find the perimeter of a quadrilateral with vertices at c (2, 4), d (1, 1), e (5, 0), and f (3, 4). round your answer to the nearest hundredth when necessary.

12.76 units
16.25 units
20.12 units
24.85 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Distance Formula", "Perimeter of Polygons", "Coordinate Geometry" ], "current_concepts": [ "Distance Formula", "Perimeter of Polygons", "Coordinate Geometry" ] } ## Calculate the lengths of the four sides using the distance formula $$ \begin{aligned} CD &= \sqrt{(1-2)^2 + (1-4)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.162 \ DE &= \sqrt{(5-1)^2 + (0-1)^2} = \sqrt{4^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \approx 4.123 \ EF &= \sqrt{(3-5)^2 + (4-0)^2} = \sqrt{(-2)^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20} \approx 4.472 \ FC &= \sqrt{(2-3)^2 + (4-4)^2} = \sqrt{(-1)^2 + 0^2} = \sqrt{1} = 1 \end{aligned} $$ ## Sum the side lengths to find the perimeter $$ \begin{aligned} \text{Perimeter} &= CD + DE + EF + FC \ &= \sqrt{10} + \sqrt{17} + \sqrt{20} + 1 \ &\approx 3.162 + 4.123 + 4.472 + 1 \ &= 12.757 \approx 12.76 \end{aligned} $$

(A) 12.76 units

(B) 16.25 units

(C) 20.12 units

(D) 24.85 units

{ "elements": [ { "type": "point", "params": [[2, 4]], "properties": { "name": "C", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 1]], "properties": { "name": "D", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[5, 0]], "properties": { "name": "E", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[3, 4]], "properties": { "name": "F", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "polygon", "params": [[2, 4], [1, 1], [5, 0], [3, 4]], "properties": { "fillColor": "rgba(140, 85, 242, 0.15)", "strokeColor": "#8C55F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the lengths of the four sides using the distance formula

Sum the side lengths to find the perimeter

Answer: