Question

the coordinates of the vertices of quadrilateral abcd are a(-1, -1), b(-3, 3), c(1, 5), and d(5, 2)
drag and drop the choices into each box to correctly complete the sentences.
the slope of \\(\overline{ab}\\) is, the slope of \\(\overline{bc}\\) is, the slope of \\(\overline{cd}\\) is, and the slope of \\(\overline{ad}\\) is
quadrilateral abcd is because

Explanation:

Step1: Calculate the slope of \(\overline{AB}\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(A(-1,-1)\) and \(B(-3,3)\), \(m_{AB}=\frac{3-(-1)}{-3 - (-1)}=\frac{4}{-2}=-2\)

Step2: Calculate the slope of \(\overline{BC}\)

For points \(B(-3,3)\) and \(C(1,5)\), \(m_{BC}=\frac{5 - 3}{1-(-3)}=\frac{2}{4}=\frac{1}{2}\)

Step3: Calculate the slope of \(\overline{CD}\)

For points \(C(1,5)\) and \(D(5,2)\), \(m_{CD}=\frac{2 - 5}{5 - 1}=\frac{-3}{4}=-\frac{3}{4}\)

Step4: Calculate the slope of \(\overline{AD}\)

For points \(A(-1,-1)\) and \(D(5,2)\), \(m_{AD}=\frac{2-(-1)}{5-(-1)}=\frac{3}{6}=\frac{1}{2}\)

Since \(m_{BC}=m_{AD}=\frac{1}{2}\), and no other pairs of slopes are equal.

Answer:

The slope of \(\overline{AB}\) is \(-2\), the slope of \(\overline{BC}\) is \(\frac{1}{2}\), the slope of \(\overline{CD}\) is \(-\frac{3}{4}\), and the slope of \(\overline{AD}\) is \(\frac{1}{2}\). Quadrilateral \(ABCD\) is a trapezoid because only one pair of opposite sides is parallel.