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Danika drew a parallelogram in a coordinate plane.

The parallelogram had no right angles.
The parallelogram is only located in quadrants III and IV.
The longest sides of the parallelogram are units long and they are parallel to the x-axis.
A vertex of one of the longest sides of the parallelogram is .
A vertex of the other longest side of the parallelogram is
Draw a parallelogram that could be the parallelogram that Danika drew.

1 answer

To create a parallelogram based on the given information, we need to follow a few steps.

  1. Identify the properties of the parallelogram:

    • Located in quadrants III and IV, so the coordinates will have negative x-values and negative y-values (for quadrant III) and negative x-values with positive y-values (for quadrant IV).
    • Longest sides are parallel to the x-axis, meaning their y-coordinates will be the same.
    • The longest sides have a specified length (we will simply denote this length as "b").
    • Given coordinate values for vertices of the longest sides will also help in constructing it.

  2. Assign coordinates for vertices:

    • Let's say one vertex on the longest side in quadrant III is at point A (-5, -2). This will be on the longer side.
    • The other vertex of the same side on the x-axis parallel opposite would then be at point B (-5 + b, -2), where "b" is the length of the longest side. Suppose we assume b = 4, then point B could be (-1, -2).

  3. Determine the positions of the other two vertices:

    • Since the parallelogram's opposite sides are equal and parallel, we will establish the height of the parallelogram. Let's say we want the height (the vertical distance between the two pairs of parallel sides) to be h (for example, h = 3).
    • From point A(-5, -2), we can move vertically upwards to create point C at (-5, -2 + h) = (-5, 1).
    • From point B (-1, -2), moving vertically to create point D at (-1, -2 + h) = (-1, 1).

  4. Summary of the vertices:

    • A: (-5, -2)
    • B: (-1, -2)
    • C: (-5, 1)
    • D: (-1, 1)

  5. Visualizing the parallelogram: To draw the parallelogram based on these points:

    • Plot points A, B, C, and D on the coordinate plane.
    • Connect points A and B, then C and D to form the bottom and top sides of the parallelogram. Connect A to C and B to D to form the vertical sides.

This gives you a parallelogram that adheres to the conditions specified: it has no right angles, occupies quadrants III and IV, and has sides oriented horizontally.

You can visualize it by marking the points and connecting them appropriately on a coordinate plane.