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.

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.

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isyllus isyllus · Answer 2 · 2019-03-28T16:10:16+01:00

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:

[tex]\text{Slope, m}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\text{Slope of AB, m}_1=\dfrac{3-3}{9+2}=0[/tex]

[tex]\text{Slope of BC, m}_2=\dfrac{6-3}{5-9}=-\dfrac{3}{4}[/tex]

[tex]\text{Slope of CD, m}_3=\dfrac{6-6}{2-5}=0[/tex]

[tex]\text{Slope of AD, m}_4=\dfrac{6-3}{2+2}=\dfrac{3}{4}[/tex]

Slope of AB = Slope of CD = 0

[tex]m_1=m_3=0[/tex]

Thus, AB is parallel to CD

Slope of BC ≠ Slope of AD

[tex]m_2\neq m_4[/tex]

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