Question

1. draw a rectangle in the coordinate plane that satisfies each of the following criteria. identify the ordered pair of each of the rectangles vertices. - the vertices lie in exactly two quadrants. - the figure has exactly two sides that are each 6 units in length. - the y-coordinates of the four vertices have the same absolute value.

Explanation:

Step1: Set y-coordinate absolute value

Choose $|y| = 3$, so $y=3$ and $y=-3$.

Step2: Assign x-values for 2 quadrants

Pick negative x (Quadrant II, III) and set two x-values: $x=-5$ and $x=-1$.

Step3: Verify side length

Calculate horizontal side length: $|-1 - (-5)| = 4$, vertical side length: $|3 - (-3)| = 6$.

Step4: List vertices

Combine x and y values to get vertices.

Answer:

One valid set of vertices is $(-5, 3)$, $(-1, 3)$, $(-1, -3)$, $(-5, -3)$ (other valid sets exist, e.g., using positive x-values like $(2,4)$, $(8,4)$, $(8,-4)$, $(2,-4)$ also meets all criteria).

To plot this:

1. Mark the four points on the coordinate plane.
2. Connect the points in order to form a rectangle.