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 .

We are given a quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

Step 1:

We find the slope of side AB.

with vertices A(-4,-5) and B(-3,0)

Hence, the slope of two points (a,b) and (c,d) is calculates as:

So, the slope of AB is:

Hence slope AB=5.

Step 2:

Now we have to find the slope of DC.

with vertices D(5,1) and C(0,2)

So, the slope of DC is:

Hence slope AB=-1/5.

Step 3:

slope of BC with vertices B(-3,0) and C(0,2) is:

Step 4:

slope of AD with vertices A(-4,-5) and D(5,1) is:

As we know that parallel sides have same slope.

As slope of BC=AD.

Hence AD is parallel to BC.

and the slope of two opposite sides are not equal hence the two sides are not parallel.

Hence, the given quadrilateral ABCD is a trapezoid. ( since it has a pair of opposite sides which are parallel and a pair of non-parallel opposite sides)

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation: