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Show that the points (-1, 1), (0, -3), (5, 2), and (4, 6) are the vertices of a parallelogram, and find its area.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
The first thing that we need to do is to get the slope of each sides of a parallelogram using the two point formula as follows
For the slope of AB:
For the slope of BC:
For the slope of CD:
For the slope of AD:
Since
then the given four points are the vertices of a parallelogram. If the slope of two lines are equal, then the two lines are parallel. Parallelogram is a closed plane figure or quadrilateral whose two opposite sides are parallel.
The area of a parallelogram is given by the formula
Substitute the values of the vertices of a parallelogram in order and solve for the value of a matrix, we have
Therefore, the area of a parallelogram is
