Answer: 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.
