Question

give the most precise classification for quadrilateral abcd.
(1 point)
trapezoid
rhombus
scalene
rectangle

Explanation:

Step1: Recall the definition of a trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides.

Step2: Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Let \(A(0,10)\), \(B(4,2)\), \(C(-2,-1)\), \(D(-6,7)\)
Slope of \(AB\): \(m_{AB}=\frac{2 - 10}{4-0}=\frac{-8}{4}=- 2\)
Slope of \(BC\): \(m_{BC}=\frac{-1 - 2}{-2 - 4}=\frac{-3}{-6}=\frac{1}{2}\)
Slope of \(CD\): \(m_{CD}=\frac{7+1}{-6 + 2}=\frac{8}{-4}=-2\)
Slope of \(DA\): \(m_{DA}=\frac{10 - 7}{0+6}=\frac{3}{6}=\frac{1}{2}\)

Since \(m_{AB}=m_{CD}=-2\), \(AB\parallel CD\)

Answer:

Trapezoid