Question

Points (1,-1), (3,2), and (7,-3) are three vertices of a parellelogram. How many parallelograms can be created using these three vertices?

One
Two
Three
Four

Answer 1

One

Explanation:

You can see this easily if you plot the three points on a graph and plot the fourth point using the fact that the sides of a parallelogram are of equal length.

Figure provided

fourth vertex D has coordinates (9,0)

We obtain this by noting that the x and y distances between A and B are
(3-1, 2-(-1) = 3, 2

= (2, 3)

Add these same dimensions to C to get point D

D = (7 +2, -3 + 3) = (9 , 0)

Only one such vertex exists which will cover the other three points