What type of figure must a quadrilateral be if its diagonals are perpendicular bisectors of each other and are congruent?

The answer is A Square

The diagonals of a square are both perpendicular bisectors and congruent. This is unique to a square. Other parallelograms, such as rectangles, have congruent diagonals, and the diagonals of a rhombus are perpendicular bisectors, but the square is the only shape that satisfies both. 

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.