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)

283 square feet

step-by-step explanation:

good luck

idn

step-by-step explanation: