Answer:
We are given a quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).
<u>Step 1:</u>
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.
<u>Step 2:</u>
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.
<u>Step 3:</u>
slope of BC with vertices B(-3,0) and C(0,2) is:
<u>Step 4:</u>
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)
