Question

Part 1: Do the points (0,0) (a,0) (a,a) and (0,a) represents a special quadrilateral? If so, which one? If not, explain why not and what should be changed? Be sure to sketch the quadrilateral. Part 2: If it does represent a special quadrilateral, use the formulas from this module to prove one of the properties from section 6.01a. Show and explain your work including a sketch to illustrate.

Answer 1

Okay, here we have this;

Considering the provided points, we are going to identify if it's a quadrilateral or not, so we obtain the following:

According to the given points it tells us that a can be any value, so if we take a=2 and plot the points we get the following:

We can see that the four points form a quadrilateral with 90 degree angles, now let's calculate the distances to know what type of quadrilateral it is:

Distance from A to B:

d=√((2-0)^2+(0-0)^2)=√4=2

Distance from B to C:

d=√((2-2)^2+(2-0)^2)=√4=2

Distance from C to D:

d=√((0-2)^2+(2-2)^2)=√4=2

Distance from D to A:

d=√((0-0)^2+(0-2)^2)=√4=2

Finally we get that it is a square because all its angles measure 90 degrees and all its sides are equal.