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Three vertices of a parallelogram are (1, 3), (0, 0), and (4, 0). Find the three possible locations of the fourth vertex.
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 |
There are three possible locations of the fourth vertex of a parallelogram. The two points or vertices can be used to draw one of the sides or one of the diagonals of a parallelogram.
Case 1: If you will use the three points or vertices to draw the two sides of a parallelogram, the fourth vertex is located at the first quadrant as shown in the figure
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| Photo by Math Principles in Everyday Life |
Since one of the sides of a parallelogram is a horizontal line that lies along the x-axis, the fourth vertex of a parallelogram is P(1 + 4, 3) or P (5, 3).
Case 2: If you will use the three points or vertices to draw the two sides of a parallelogram, the fourth vertex is located at the second quadrant as shown in the figure
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| Photo by Math Principles in Everyday Life |
Since one of the sides of a parallelogram is a horizontal line that lies along the x-axis, the fourth vertex of a parallelogram is P(1 - 4, 3) or P (-3, 3).
Case 3: If you will use the three points or vertices to draw the two diagonals of a parallelogram, the fourth vertex is located at the fourth quadrant as shown in the figure
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| Photo by Math Principles in Everyday Life |
The center of a parallelogram which is the intersection of two diagonals bisects the diagonals into two equal parts. In this case, the midpoint of a diagonal that lies along the x-axis is (2, 0). If the midpoint of the other diagonal is also (2, 0), then we can solve for the coordinates of the other end of other diagonal which the fourth vertex of a parallelogram as follows
