Question

16. For quadrilateral ABCD, determine the most precise name for it. A (-2, 3), B (9, 3), C (5, 6) and D (2, 6). Show your work and explain.

Answer 1

Answer:

Trapzoid

Step-by-step explanation:

Given: A (-2, 3), B (9, 3), C (5, 6) and D (2, 6)

We will find the slope of each line.

Formula:

$\text{Slope, m}=\dfrac{y_2-y_1}{x_2-x_1}$

$\text{Slope of AB, m}_1=\dfrac{3-3}{9+2}=0$

$\text{Slope of BC, m}_2=\dfrac{6-3}{5-9}=-\dfrac{3}{4}$

$\text{Slope of CD, m}_3=\dfrac{6-6}{2-5}=0$

$\text{Slope of AD, m}_4=\dfrac{6-3}{2+2}=\dfrac{3}{4}$

Slope of AB = Slope of CD = 0

$m_1=m_3=0$

Thus, AB is parallel to CD

Slope of BC ≠ Slope of AD

$m_2\neq m_4$

Thus, BC is not parallel to AD

The quadrilateral ABCD has two sides are parallel and two are not parallel.

Hence, The quadrilateral is trapzoid

Answer 2

The quadrilateral ABCD, with vertices A(-2,3), B(9,3), C(5,6) and D(2, 6), is a trapezoid. 

 By definition, a trapezoid is a quadrilateral which has two parallel sides (These are called "bases"), but the other sides are not parallels.