Question

If 3 vertices of a rectangle are (0, 0), (2, 0), and (0, 3), find the coordinates of the 4th vertex?

Answer 1

Mid point of (0,0) and(0,3)
midpoint =0+0/2=0
&0+3/2=3/2
midpoint is (0,3/2)
then it is also the midpoint of (2,0) and the vertex
let the vertex be (a,b)
a+2/2=0 therfore a=-2
b+0/2=3/2 therfore b is 3
therefore the vertex is (-2,3)

Answer 2

Following the method used in the previous answer to this question, we have a general result concerning a parallelogram.
Let the vertices of a parallelogram be $(x_1,y_1), (x_2,y_2), (x_3,y_3), (x_4,y_4).\\ \mathrm{Then} \\ x_1+x_3=x_2+x_4\\ y_1+y_3=y_2+y_4$
And we can solve it directly.