Question

show that points A B C D are vertices of a square.
A=(1,-3) B=(-8,1) C=(-4,10) D=(5,6)

Answer 1

you have to show that the sides are equal and perpendicular

Answer 2

If you know something about vectors, the solution is slightly easier, computationally. Compute the vectors BC, CD, AB, and AD. Then show via the dot product that BC and CD are orthogonal, that AD and CD are orthogonal, and that BA and AD are orthogonal. 3 right angles suffices to conclude four right angles via some easy geometric proofs.

Then show that the norm of BC and AD are equal and that the norm of CD and AB are equal.

Answer 3

i dont know anything about vectors.

Answer 4

Well, that's harder. Like tomo suggested, you have to prove the sides are equal in length and orthogonal. I graphed the points to get a rudimentary understanding of the location of the points.

to show that the side lengths are equal, you merely have to show BC = CD and AB = BC because by transitivity, you will end up AB = CD. That's manageable with the distance formula (do you know this formula?)

to show that the side lengths are orthogonal, you have to show the slopes of the line segments are negative reciprocals of each other--e.g., if one slope is 4, then the other slope MUST be -1/4. You have to compute the slopes of all 4 line segments: AB, BC, CD, AD, though, I'm afraid.