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On a coordinate plane, quadrilateral A B C D is shown. Point A is at (negative 4, negative 5), point B is at (negative 3, 0), point C is at (0, 2), and point D is at (5, 1).

Determine whether quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1) is a trapezoid.



Step 1: Find the slope of AB. The slope of AB is .




Step 2: Find the slope of DC. The slope of DC is .




Step 3: Find the slope of BC. The slope of BC is .




Step 4: Find the slope of AD. The slope AD is .




The quadrilateral is a trapezoid because

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Answer:

The quadrilateral is a trapezoid because contiguous lines are perpendicular

Step-by-step explanation:

Remember that two lines are perpendicular when the products of their slopes is -1

Step1

[tex]{\displaystyle \text{SlopeAB} = \frac{0+5}{-3+4} = 5[/tex]

Step2

[tex]{\displaystyle \text{SlopeDC} = \frac{1-2}{5-0} = \frac{-1}{5} = -\frac{1}{5}[/tex]

Step3

[tex]{\displaystyle \text{SlopeBC} = \frac{2-0}{0-3} = \frac{2}{-3} = -\frac{2}{3}[/tex]

Step4

[tex]{\displaystyle \text{SlopeAD} = \frac{5+4}{1+5} = \frac{9}{6} = \frac{3}{2}[/tex]

The quadrilateral is a trapezoid because contiguous lines are perpendicular

Answer:

step 1 : 5

step 2 : - 1/5

step 3 : 2/3

step 4 : 2/3

The quadrilateral is a trapezoid because only one pair of opposite sides is parallel.

Step-by-step explanation:

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