Graph and identify the coordinates of a rectangle with a length of at least 5 units and a width of at least 2 units. Each vertex of the rectangle must be in a different quadrant. Two of the points must have rational coordinates that are not integers.

Question

Graph and identify the coordinates of a rectangle with a length of at least 5 units and a width of at least 2 units. Each vertex of the rectangle must be in a different quadrant. Two of the points must have rational coordinates that are not integers.

I'm not sure what to do. Please don't give me the answer just an example.

Thanks

Answer 1

21/2 is rational but not integer and it is more than 5 and more than 2

so a square would solve the problem.
put points at (21/2, 21/2) in quadrant 1
then its image (-21/2, 21/2) in quadrant 2
then (-21/2, -21/2) in quadrant 3
and (21/2,-21/2) in quadrant 4.

Answer 2

To graph and identify the coordinates of a rectangle with the given conditions, we can break down the process into steps:

Step 1: Understand the Quadrants
Before we begin, let's review the four quadrants on a coordinate plane:
- Quadrant I: (+, +)
- Quadrant II: (-, +)
- Quadrant III: (-, -)
- Quadrant IV: (+, -)

Step 2: Determine the Length and Width
Since we need a rectangle with a length of at least 5 units and a width of at least 2 units, we can choose any two sides that satisfy these conditions. For this example, let's assume the length is along the positive x-axis and the width is along the positive y-axis.

Step 3: Determine the First Point
To have rational coordinates that are not integers, we can choose a point on the x-axis that lies in Quadrant I. For simplicity, let's select the point (5, 0), which lies on the x-axis in Quadrant I.

Step 4: Determine the Second Point
We need to find a point on the y-axis in Quadrant II to complete one of the shorter sides of the rectangle. Let's select the point (0, 2), which lies on the y-axis in Quadrant II.

Step 5: Determine the Third Point
To find a point on the x-axis in Quadrant III that completes the longer side of the rectangle, we can select the point (-5, 0), which lies on the x-axis in Quadrant III.

Step 6: Determine the Fourth Point
Lastly, we need to find a point on the y-axis in Quadrant IV to complete the other shorter side of the rectangle. Let's select the point (0, -2), which lies on the y-axis in Quadrant IV.

Step 7: Plot the Points
Now that we have determined the four points, we can plot them on a coordinate plane:
- (5, 0) in Quadrant I
- (0, 2) in Quadrant II
- (-5, 0) in Quadrant III
- (0, -2) in Quadrant IV

By following these steps, you should be able to graph a rectangle that meets all the given conditions. Make sure to label the coordinates of each point on the graph for reference.