Respuesta :
A pair of coordinates is given by (x,y)
The given coordinates of the vertices of the quadrilateral are:
A (-1, -1)
B (-3, 3)
C (1, 5)
D (5, 2)
To find the slope of a segment we can use the next formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where m is the slope, and (x1, y1) and (x2, y2) are two points of the line.
The slope of AB:
[tex]\begin{gathered} m=\frac{3-(-1)}{-3-(-1)}=\frac{3+1}{-3+1}=\frac{4}{-2} \\ m=-2 \end{gathered}[/tex]Thus, the slope of AB is -2.
The slope of BC:
[tex]\begin{gathered} m=\frac{5-3}{1-(-3)}=\frac{5-3}{1+3}=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]Thus, the slope of BC is 1/2.
The slope of CD:
[tex]\begin{gathered} m=\frac{2-5}{5-1}=\frac{-3}{4} \\ m=-\frac{3}{4} \end{gathered}[/tex]Thus, the slope of CD is-3/4.
The slope of DA:
[tex]\begin{gathered} m=\frac{-1-2}{-1-5}=\frac{-3}{-6} \\ m=\frac{1}{2} \end{gathered}[/tex]Thus, the slope of DA is 1/2.
Knowing the slopes of the sides, we can conclude that side BC is parallel to side DA, since they have the same slope 1/2 (remember that parallel lines have equal slope) but side AB is not parallel to CD since they have different slopes.
A parallelogram has two pairs of parallel sides, then quadrilateral ABCD is not a parallelogram.
A trapezoid is a quadrilateral that has one pair of parallel sides, thus quadrilateral ABCD is a trapezoid since only one pair of opposite sides is parallel.
