Question

A student graphs three of the four vertices of parallelogram ABCD. Which point could be the fourth vertex of the parallelogram?

Answer 1

The point (6, 3) will make this a parallelogram.

In a parallelogram, both pairs of opposite sides are parallel.  From the choices we have for point D, we want to find the coordinates of the point so that the slope from B to D is the same as the slope from A to C, since parallel lines have the same slope.

m = (y₂-y₁)/(x₂-x₁) = (3-0)/(3-0) = 3/3 = 1 (from point A to C)

This means that for every 1 we go up from point B, we want to go 1 right as well.  3 up and 3 right will get us the point (6, 3), which will give BD the same slope as AC.