(−4, 5)
(4, 5)
(−3, 4)
(0, 11)
The correct answer is :A
Since ABCD is a parallelogram, opposite sides are parallel and have the same length. The midpoint formula can be used to find the midpoint of a line segment given its endpoints.
First, let's find the midpoint of AB:
Midpoint of AB=
Next, let's find the midpoint of BC:
Midpoint of BC===(0.5, 6)
Now, since opposite sides of a parallelogram are parallel, the vector from A to B is equal to the vector from D to C. We can use this information to find the coordinates of point D.
Vector from A to B: (3-1, 4-1)=(2,3)
Coordinates of C: (-2, 8)
Now, we can add the vector AB to the coordinates of C to find D:
D = C + AB = (-2 + 2, 8 + 3) = (0, 11)
So, the correct answer is:
The coordinates of the vertex D are (0, 11).
When two diagonals in a parallelogram bisect one another, it means that the midpoints of both diagonals are the same.
Midpoint of AC =
Let vertex D's coordinates be
and