Question

The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex? What are coordinates of the fourth vertex?

Answer 1

To find the position of the fourth vertex of a parallelogram, we can use the properties of a parallelogram. In this case, the fourth vertex has coordinates (5, 4) and there is only one possibility for its position.

Step-by-step explanation:

To find the possibilities for the position of the fourth vertex, we need to understand the properties of a parallelogram. In a parallelogram, opposite sides are parallel and congruent. Therefore, to find the fourth vertex, we can use the following logic:

1. We know the coordinates of three vertices: A(2, 0), B(4, 3), and C(3, 1).

2. Find the difference between points B and A, which is (4-2, 3-0) = (2, 3).

3. Add this difference to the coordinates of point C to find the fourth vertex: C + (2, 3) = (3+2, 1+3) = (5, 4).

Therefore, the fourth vertex has coordinates (5, 4). Since the opposite sides of a parallelogram are congruent, there is only one possibility for the position of the fourth vertex.

Answer 2

probability is one for the position of the fourth vertex

it's co ordinates will be (2,2)