MATH SOLVE

2 months ago

Q:
# Need help with this question! Julia is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning coordinates as given. Drag and drop the correct answer into each box to complete the proof.The coordinates of point C are (__, c).The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (__, c/2 ).The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are ( a+b/2, __).AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (a+b/2, c/2) .By the definition of midpoint, AE¯¯¯¯¯≅ __ and BE¯¯¯¯¯≅ __.Therefore, diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other. Options: 1. a + b 2. a + c 3. b + c 4. a+b/2 5. a−b/2 6. a/2 7. b/2 8. c/2 9. AC¯¯¯¯¯ 10. BD¯¯¯¯¯ 11. CE¯¯¯¯¯ 12. DE¯¯¯¯¯

Accepted Solution

A:

The coordinates of point C are (a + b, c).

The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (a+5/2, c/2 ).

The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are ( a+b/2, c/2).

By the definition of midpoint, AE¯¯¯¯¯≅ CE and BE¯¯¯¯¯≅ DE.

The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (a+5/2, c/2 ).

The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are ( a+b/2, c/2).

By the definition of midpoint, AE¯¯¯¯¯≅ CE and BE¯¯¯¯¯≅ DE.