Question

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Answer 1

The slope of AB is -2
The slope of BC is 1/2
The slope of CD is -3/4
The slope of AD is 1/2
The quadrilateral ABCD is a trapezoid because only one pair of opposite sides are parallel. YOU'RE WELCOME :D

Answer 2

ANSWER TO QUESTION 1

The Vertex A has coordinates $(-1,-1)$ and the vertex B has coordinates  $(-3,3)$.

The slope of AB can be determined using the formula;

$Slope_{AB}=\frac{y_2-y_1}{x_2-x_1}$

Where $(x_1,y_1)=A(-1,-1)$ and $(x_2,y_2)=B(-3,3)$.

Plugging these values in to the formula gives;

$Slope_{AB}=\frac{3--1}{-3--1}$

$Slope_{AB}=\frac{3+1}{-3+1}$

$Slope_{AB}=\frac{4}{-2}$

$Slope_{AB}=-2$

ANSWER TO QUESTION 2

The Vertex B has coordinates $(-3,3)$ and the vertex C has coordinates  $(1,5)$.

The slope of BC can be determined using the formula;

$Slope_{BC}=\frac{y_2-y_1}{x_2-x_1}$

Where $(x_1,y_1)=B(-3,3)$ and $(x_2,y_2)=C(1,5)$.

Plugging these values in to the formula gives;

$Slope_{BC}=\frac{5-3}{1--3}$

$Slope_{BC}=\frac{5-3}{1+3}$

$Slope_{BC}=\frac{5-3}{1+3}$

$Slope_{BC}=\frac{2}{4}$

$Slope_{BC}=\frac{1}{2}$

ANSWER TO QUESTION 3

The Vertex C has coordinates $(1,5)$ and the vertex D has coordinates  $(5,2)$.

The slope of CD can be determined using the formula;

$Slope_{CD}=\frac{y_2-y_1}{x_2-x_1}$

Where $(x_1,y_1)=C(1,5)$ and $(x_2,y_2)=D(5,2)$.

Plugging these values in to the formula gives;

$Slope_{CD}=\frac{2-5}{5-1}$

$Slope_{CD}=\frac{-3}{4}$

$Slope_{CD}=-\frac{3}{4}$

ANSWER TO QUESTION 4

The Vertex A has coordinates $(-1,-1)$ and the vertex D has coordinates  $(5,2)$.

The slope of AD can be determined using the formula;

$Slope_{AD}=\frac{y_2-y_1}{x_2-x_1}$

Where $(x_1,y_1)=A(-1,-1)$ and $(x_2,y_2)=D(5,2)$.

Plugging these values in to the formula gives;

$Slope_{AD}=\frac{2--1}{5--1}$

$Slope_{AD}=\frac{2+1}{5+1}$

$Slope_{AD}=\frac{3}{6}$

$Slope_{AD}=\frac{1}{2}$

ANSWER TO QUESTION 5.

When we examine the slopes carefully we can see that

$Slope_{AD}=\frac{1}{2}=Slope_{BC}$.

Whenever the slopes of two straight lines  are the same, it means the two lines are parallel.

Since quadrilateral ABCD has one pair of opposite sides parallel and the pair of opposite sides not parallel, the quadrilateral is a trap-ezoid.

Hence the answer is :

Quadrilateral ABCD is a trap-ezoid because only one pair of opposite side is parallel.