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

Trapzoid

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}=(y_2-y_1)/(x_2-x_1)`

`\text{Slope of AB, m}_1=(3-3)/(9+2)=0`

`\text{Slope of BC, m}_2=(6-3)/(5-9)=-(3)/(4)`

`\text{Slope of CD, m}_3=(6-6)/(2-5)=0`

`\text{Slope of AD, m}_4=(6-3)/(2+2)=(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\\eq 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.