1)
The given vertices of the quadrilateral are
L(- 5, 1), M(- 2, - 2), N(- 1, - 3), O(2, - 2)
We would find the slope of the lines connecting the pairs of vertices. Recall, the opposite sides of a parallelogram are parallel. This means that they would have the same slope. The formula for calculating slope is expressed as
slope = (y2 - y1)/(x2 - x1)
Considering L(- 5, 1) and M(- 2, 2),
x1 = - 5, y1 = 1
x2 = - 2, y2 = 2
slope = (2 - 1)/(- 2 - - 5) = 1/(- 2 + 5) = 1/3
Slope of LM = 1/3
Considering N(- 1, - 3) and O(2, - 2)
x1 = - 1, y1 = - 3
x2 = 2, y2 = - 2
slope = (- 2 - - 3)/(2 - - 1) = (- 2 + 3)/(2 + 1) = 1/3
Slope of NO = 1/3
Since the slopes of the opposite sides are equal, it is a parallelogram
We would plot the coordinates of the vertices on a graph as shown below.
