Exercise 31 Page 203

We are given the vertices of quadrilateral ABCD. &A(-3,1) && B(1,-2) &C(0,-3) && D(-4,0) To determine whether the opposite sides of the quadrilateral are parallel, we will begin by plotting the vertices and drawing the sides.

Now, let's find the slope of each side using the Slope Formula. m=y_2- y_1/x_2- x_1 In the formula, ( x_1, y_1) and ( x_2, y_2) are two points on the segment. We will start with the segment AB.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -3,1) & ( 1,-2)

m=-2- 1/1-( -3)

SubNeg

a-(- b)=a+b

m=-2-1/1+3

AddSubTerms

Add and subtract terms

m=-3/4

MoveNegNumToFrac

Put minus sign in front of fraction

m=-3/4

The slope of AB is - 34. We will find the slopes of the other sides in the same way.

Sides	Endpoints	m=y_2-y_1/x_2-x_1	Slope
AB	A( -3, 1), B( 1, -2)	m=-2- 1/1-( -3)	m=-3/4
BC	B( 1, -2), C( 0, -3)	m=-3-( -2)/0- 1	m=1
CD	C( 0, -3), D( -4, 0)	m=0-( -3)/-4- 0	m=-3/4
DA	D( -4, 0), A( -3, 1)	m=1- 0/-3-( -4)	m=1

The opposite sides of the quadrilateral, AB and CD as well as BC and DA, have the same slopes. Because lines with the same slope are parallel, we know that the opposite sides are parallel.