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¯¯¯¯¯

1. 1 2. 4 3. 8 4. AC,  BD 5. CE, DE 6.

Step-by-step explanation:

Below each answer the respective explanation, and also a numerical coordinate parallelogram just to make it clearer.

According to the graph

A= (0,0)

B= (a,0)

C= (a+b, c)

D=(b,c)

E=(a+b/2, c/2)

1. The coordinates of point C are

To find the x-coordinate of C: just add a to b

2. The coordinates of the midpoint of diagonal AC are (__, c/2 ).

Midpoints are calculated by:

Since A (0,0) and C (a+b,c) Then: (a+b/2, c/2)

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

Then (8)

4. ___ and ___ intersect at point E with coordinates (a+b/2, c/2)

AC and BD . True. This is a consequence of steps 2 and 3.

5. By the definition of midpoint, AE≅ __ and BE≅ __.

6.Therefore, diagonals AC and BD bisect each other.

In this sense, to bisect is to equally divide into two congruent line segments.

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