Rectangle Space:width-height plane

In the right panel is a picture of a rectangle with a given height and width and therefore a well-defined Area and Perimeter. In the left panel is a graph of height vs. width, with a RED dot at a position that corresponds to the height and width of the rectangle in the right panel. You can change the rectangle by dragging the RED dot. You can leave a mark at the current position by clicking the "mark this point" button. [you may need graph paper to answer the following questions] along what curve in the height-width plane are all the ▪ squares? ▪ similar rectangles? ▪ rectangles of a given perimeter? ▪ rectangles of a given area? ▪ rectangles whose diagonal has a given value? Make up another question to ask.