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 sl

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3 years ago

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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 sl

ope 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

Mathematics

2 answers:

Pani-rosa [81] · Answer 1 · 2022-04-19T00:14:22+03:00

Pani-rosa [81]3 years ago

7 0

Answer:

The Slope of AB: 5/1

The Slope of DC: -1/5

The Slope of BC: 2/3

The Slope of AD: 2/3

The quadrilateral is a trapezoid because BC and AD are parallel to each other while AB and DC are congruent.

Step-by-step explanation:

Stels [109] · Answer 2 · 2022-04-19T02:35:59+03:00

Answer: Yes, the quadrilateral ABCD is a TRAPEZOID.

Step-by-step explanation: Given that the co-ordiantes of the vertices of quadrilateral ABCD are A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

We are to determine whether the quadrilateral ABCD is a trapezoid or not.

TRAPEZOID: It is a quadrilateral having one pair of opposite sides parallel.

We will find the slopes of all the sides AB, BC, CD and DA of quadrilateral ABCD as follows:

$\textup{slope of AB}=\dfrac{0-(-5)}{-3-(-4)}=\dfrac{5}{1}=5,\\\\\\\textup{slope of BC}=\dfrac{2-0}{0-(-3)}=\dfrac{2}{3},\\\\\\\textup{slope of CD}=\dfrac{1-2}{5-0}=\dfrac{-1}{5}=-\dfrac{1}{5},\\\\\\\textup{slope of DA}=\dfrac{-5-1}{-4-(-5)}=\dfrac{-6}{-9}=\dfrac{2}{3}.$

Since the slopes of sides BC and DA are equal, so the sides are parallel.

Hence, the quadrilateral ABCD has one pair of opposite sides parallel.

Thus, quadrilateral ABCD is a TRAPEZOID.