The verticals of quadrilateral ABCD are given. Draw ABCD i'n a coordinate plane and show that it is a parallelogram
To draw quadrilateral ABCD on a coordinate plane and show that it is a parallelogram, we need to determine the coordinates of its vertices based on the given information about its verticals. Let's walk through the process step by step:
1. Identify the given information about the verticals of quadrilateral ABCD. This refers to the pairs of opposite sides that are parallel to the y-axis.
2. Let's assume the verticals given are AB and CD. We need to know the coordinates of the points A, B, C, and D to draw the quadrilateral.
3. Choose any convenient value for the x-coordinate for A and C. Let's say we choose x = 0 for both A and C.
4. Now, based on the given information that AB and CD are verticals, we know that the x-coordinate of point B should be the same as the x-coordinate of point A. Similarly, the x-coordinate of point D should be the same as the x-coordinate of point C. So, set the x-coordinate of B and D to be 0 as well.
5. To complete the information, we need the y-coordinates of A, B, C, and D. These can be any values, but they should be consistent with the fact that AB and CD are verticals. Let's say A has a y-coordinate of a, B has a y-coordinate of b, C has a y-coordinate of c, and D has a y-coordinate of d.
6. Therefore, the coordinates of the four vertices of the quadrilateral ABCD are as follows:
A(0, a)
B(0, b)
C(0, c)
D(0, d)
7. Plot the four points on the coordinate plane based on their coordinates.
8. Finally, observe the shape formed by the points A, B, C, and D. If the opposite sides AB and CD are parallel, then ABCD is a parallelogram. Verify that the opposite sides appear parallel by visually inspecting the drawn quadrilateral on the coordinate plane. If the opposite sides have the same slope or are vertical lines, it confirms that ABCD is a parallelogram.
By following these steps and plotting the points, you can draw quadrilateral ABCD on the coordinate plane and visually demonstrate that it is a parallelogram.