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A base of a parallelogram is on the x-axis and the origin is located at the left endpoint of that base. Three consecutive vertic
es are (h, j), (0, 0), and (k, 0), where h > 0. How many units to the right of a vertical line through (k, 0) must the fourth vertex be?
1 answer:
If you illustrate the problem, the parallelogram will look like this with the following coordinated (see picture).
The k must be the x-axis while h must be the y-axis. The y-coordinate of the unknown must be j because it is aligned with the upper right corner. By definition, a parallelogram is a quadrilateral with two equal, parallel sides. Hence,you also have two sets of equal angles. It also means that the distance of the upper and bottom corners of the left side and the right side are equal. Through symmetry, the x-coordinate is the distance between h and k.
Thus, the unknown coordinates are (h-k,j)
The k must be the x-axis while h must be the y-axis. The y-coordinate of the unknown must be j because it is aligned with the upper right corner. By definition, a parallelogram is a quadrilateral with two equal, parallel sides. Hence,you also have two sets of equal angles. It also means that the distance of the upper and bottom corners of the left side and the right side are equal. Through symmetry, the x-coordinate is the distance between h and k.
Thus, the unknown coordinates are (h-k,j)
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