8. GRAPHING THE RELATION OF TWO GEOMETRIC QUANTITIES DIRECTLY--WITHOUT WRITING AN EQUATION.

Given triangle ABC. Let C move along a line segment DE. How does the area change as C moves? Think about DE being parallel to AB. Then DE not parallel.

With Sketchpad you can compare DC and the Area in several ways.

You can animate the figure as C moves along DE, and watch the area change

You can graph the relation of Area(ABC) to some specific length: such as the length of AC, or the distance DC.

· What would a graph of Area(ABC) vs. DC look like? Why?

· What would a graph of Area(ABC) vs. AC look like? Why?

· How do the graphs change If DE Is not parallel to AB? Why?

You can use the coordinate axes on Sketchpad and plot point (x,y) using y = Area and x = length. Or, you can construct our own geometrical representation of Area vs. length

Here we have plotted Area of Triangle ABC vs. DC.

Why does the graph turn around?

For what position of C does it turn around?

Here we have plotted:

Area (BAC) vs. CA thick curve

Area (BAC) vs CD linear

CA vs CD thin curve

How do you make sense of the relation of the three plotted points as C moves along DE?

Try plotting (for DE parallel to AB):

Area (BAC) vs. CA thick line

Area (BAC) vs CD thick line

CA vs CD thin curve

Notice that the Area vs. CA or CD gives same line, but the locus point is different. This shows up as you move C.