Answer :
Answer: Yes, the quadrilateral ABCD is a trapezoid.
Step-by-step explanation: Given that the vertices of the quadrilateral ABCD are A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).
We are to determine whether ABCD is a trapezoid or not.
We know that a trapezoid is a quadrilateral with one pair of opposite sides parallel. Also, the slopes of two parallel lines are equal.
First, we will find the slopes of the sides AB, BC, CD and DA.
We have
[tex]\textup{Step 1: The slope of AB}=\dfrac{0+5}{-3+4}=\dfrac{5}{1}=5,\\\\\textup{Step 2: The slope of BC}=\dfrac{2-0}{0+3}=\dfrac{2}{3},\\\\\textup{Step 3: The slope of CD}=\dfrac{1-2}{5-0}=-\dfrac{1}{5},\\\\\textup{Step 4: The slope of DA}=\dfrac{-5-1}{-4-5}=\dfrac{2}{3}.[/tex]
Since the slopes of the sides BC and DA are equal, so BC an DA are the parallel sides of the quadrilateral ABCD.
Thus, the quadrilateral is a trapezoid because it has a pair of opposite sides parallel.
The quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.
What is a trapezoid?
It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
We have:
Quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1)
To identify the quadrilateral is a trapezoid we must find the slopes of the lines AB, BC, Cd, and AD
For slope m the formula is given by:
[tex]\rm m = \frac{y_2-y_1}{x_2-x_1}[/tex]
For slope of AB:
[tex]=\rm \frac{0-(-5)}{-3-(-4)}[/tex]
[tex]=\rm \frac{0+5}{-3+4}[/tex]
= 5
For slope of BC:
[tex]=\rm \frac{2-0}{0-(-3)}[/tex]
[tex]=\rm \frac{2}{3}[/tex]
For slope of CD:
[tex]=\rm \frac{1-2}{5-0}[/tex]
= -1/5
For slope of AD:
[tex]=\rm \frac{-5-1}{-4-5}[/tex]
= 2/3
Because the slopes of the sides BC and DA are equivalent, BC and DA are the quadrilateral ABCD's parallel sides.
Thus, the quadrilateral is a trapezoid because it contains two opposite sides that are parallel, the quadrilateral is called a trapezoid.
Learn more about the trapezoid here:
brainly.com/question/8643562
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