SOLUTION: Find a point D(x, y) such that the points A(-3,0), B(4,-1), C(0,-4), and D are the corners of a square. (If an answer does not exist, enter DNE.)

A(-3,0), B(4,-1), C(0,-4), and D

Let's plot them and see:

 

That looks like they could be corners of a square. Let's draw a couple 
of right triangles:



The blue right triangle and the green right triangle are congruent
because they each have a side that's 3 units long and a side that's
4 units. long.  So the hypotenuses are equal in length.  So there has 
to be a right angle at C(0,-4) because the angles at C(0,-4) are 
complementary. So what you have to do is to create another pair of
right triangles congruent to each of those like the red one and the
black one below.



And as you see, the point D has to be D(1,3)

Edwin