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

the coordinate point C are (a+b,c)

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

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

AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates ​(a+b/2, c/2)​

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

Step-by-step explanation:

The coordinates of the midpoint of diagonal AC are . The coordinates of the midpoint of diagonal BD are   AC and BD  intersect at point E with coordinates . By the definition of midpoint, CE ≅ EA and BE ≅ ED Therefore, diagonals AC and BD bisect each other.

Step-by-step explanation:

Since, here the coordinates of A ≡ (0,0) B ≡ (a, 0) D≡ ( b,c)

And, here ABCD is the parallelogram.

Therefore AB = CD

If y is the y-coordinate of C Then C≡(a+b, y)

⇒

⇒ y =c

Thus, C≡(a+b, c)

The coordinates of the midpoint of diagonal AC are,

And,  The coordinates of the midpoint of diagonal BD are,

Since, by the below diagram AC and BD are intersecting at point E,

Where the  coordinates of E are,

Thus, E is the mid point of Both the segments AC and BD

Because, BE = ED and AE = EC

Therefore, we can say that both AC and BD bisect each other.

there are no short passages to look at