Copy of Co-variation & Invariance: Area of a Rectangle
This applet can model this situation: "A rectangle has a fixed area. If its length is 24 cm, it width is 7 cm. In general, the length is x cm and the width is y cm."
Part 1: Move point A and predict what will happen to point B. When you move the point A from the origin O horizontally, you will notice that point B moves from the origin O vertically. We can use the letter x to represent the independent variable which is the length of the horizontal line segment OA (i.e., the distance point A is from the origin). We can use the letter y to represent the dependent variable which is the length of the vertical line segment OB (i.e., the distance point B is from the origin).
Part 2: Turn "Show Point" on to reveal the position of point C. Point C is a way to represent both the x-value and the y-value simultaneously. That means that the point C shows a specific instance of the two related quantities. For example, when x is 24, y is 7.
Part 3: Turn "Show Function" on to reveal the where all possible point C can lie.
1. How many cm is the length if the width is 21 cm?
2. How are the two quantities x and y related?
3. What is invariant? (a) sum of the two quantities x + y, (b) difference between the two quantities x - y, (c) product of the two quantities xy, or (d) ratio of the two quantities y/x? Why?