lorrainelopez
03.07.2020 •
Mathematics
The diagonals of quadrilateral ABCD intersect at E(−2,4). ABCD has vertices at A(1,7) B(−3,5). What must be the coordinates of C and D to ensure that ABCD is a parallelogram?
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Ответ:
The coordinates of C and D are (1, 3) and (-5, 1), respectivelly.
Step-by-step explanation:
Since E is the midpoint of diagonals AD and BC (see attachment). That is:
The vectorial distances of AE and BE are, respectively:
Now, the relative vectorial distances to C and D are now obtained:
Lastly, the coordinates are found by the following vectorial equations:
The coordinates of C and D are (1, 3) and (-5, 1), respectivelly.
Ответ: