How do you prove that quadrilateral ABCD is a parallelogram with A(-2,-1) B(1,2) C(5,2) D (2,-1) using slope?

Question

Jayden Jackson · Accepted Answer

Please see below.

With corners as #A(-2,-1)#, #B(1,2)#, #C(5,2)# and #D(2,-1)#, let us find slopes of each side of the parallelogram #ABCD#. Slope of #AB# is #(2-(-1))/(1-(-2))=3/3=1# Slope of #BC# is #(2-2)/(5-1)=0/4=0# Slope of #CD# is #((-1-2)/(2-5)=(-3)/(-3)=1# Slope of #DA# is #(-1-(-1))/(2-(-2))=0/4=0# As slopes of alternate sides of quadrilateral are equal, alternate sides are parallel to each other and #ABCD# is a parallelogram.

Evelyn Arboleda · Answer

undefined To prove that quadrilateral ABCD is a parallelogram using slopes, we need to show that the slopes of opposite sides are equal.

1. Find the slopes of the line segments AB, BC, CD, and DA using the formula:
$$ \text{Slope} = \frac{{\text{change in }} y}{{\text{change in }} x} $$

2. Calculate the slopes for segments AB, BC, CD, and DA.

3. Show that the slopes of opposite sides are equal:
$$ \text{Slope of AB} = \text{Slope of CD} $$
$$ \text{Slope of BC} = \text{Slope of DA} $$

If the slopes of opposite sides are equal, then the quadrilateral ABCD is a parallelogram.

Performing these steps will demonstrate that ABCD is a parallelogram based on the equality of slopes of opposite sides.