Answer:
The most precise name for a quadrilateral ABCD is a parallelogram
Step-by-step explanation:
step 1
Draw the figure
we have that
The coordinates of a quadrilateral are
A(-5,2),B(-3,5), C(4,5) and D(2,2)
using a graphing tool
Plot the coordinates to better understand the problem
see the attached figure
step 2
<em>Find the length sides of the quadrilateral</em>
the formula to calculate the distance between two points is equal to
<em>Find the length side AB</em>
A(-5,2),B(-3,5)
substitute in the formula
<em>Find the length side CD</em>
C(4,5), D(2,2)
substitute in the formula
<em>Find the length side AD</em>
A(-5,2), D(2,2)
substitute in the formula
<em>Find the length side BC</em>
B(-3,5), C(4,5)
substitute in the formula
step 3
<em>Find the slope of the length sides of the quadrilateral</em>
The formula to calculate the slope between two points is equal to
<em>Find the slope of the length side AB</em>
A(-5,2),B(-3,5)
substitute in the formula
<em>Find the slope of the length side CD</em>
C(4,5), D(2,2)
substitute in the formula
<em>Find the slope of the length side AD</em>
A(-5,2), D(2,2)
substitute in the formula
----> is a horizontal line
<em>Find the slope of the length side BC</em>
B(-3,5), C(4,5)
substitute in the formula
substitute in the formula
----> is a horizontal line
step 4
Compare the length sides
opposite sides are congruent
step 5
Compare the slopes
Remember that
If the lines are parallel, then their slopes are the same
so
opposite sides are parallel
therefore
The most precise name for a quadrilateral ABCD is a parallelogram