Crystal is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning c

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Crystal is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning c

oordinates as given. A parallelogram graphed on a coordinate plane. The parallelogram is labeled A B C D. The coordinates of vertex A are 0 comma 0. The coordinates of vertex B a comma 0. The coordinates of vertex C are not labeled. The coordinates of vertex D are b comma c. Diagonals A C and B D intersect at point E whose coordinates are not labeled. Drag and drop the correct answer into each box to complete the proof. The coordinates of point C are (a + b,). The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are ( a+b2 ,). The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are (a+b2, c2) . AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (, c2 ). By the definition of midpoint, ≅CE¯¯¯¯¯ and BE¯¯¯¯¯≅ . Therefore, diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.

Mathematics

2 answers:

irina [24] · Answer 1 · 2022-02-07T17:42:39+03:00

Answer: The coordinates of the midpoint of diagonal AC are $(\frac{a+b}{2} , \frac{c}{2} )$ . The coordinates of the midpoint of diagonal BD are $(\frac{a+b}{2} , \frac{c}{2} )$ AC and BD intersect at point E with coordinates $(\frac{a+b}{2} , \frac{c}{2} )$ . By the definition of midpoint, CE ≅ EA and BE ≅ ED Therefore, diagonals AC and BD bisect each other.