Sketching out the shape shows us that it is neither a square nor rectangle (alternatively, we could tell from the points since if it was a rectangle/square, there would be two sets of x co-ordinate values and y-co-ordinate values only).
Find the length of MN:
MN²=(Yn-Ym)²+(Xn=Xm)²
MN²=(4-1)²+(3-1)²
MN²=3²+2²
MN²=9+4
MN=√13
Find the length of MP:
MP²=(Yp-Ym)²+(Xp-Xm)²
MP²=(3-1)²+(4-1)²
MP²=2²+3²
MP²=4+9
MP=√13
Since the side lengths are equal, the shape must be a rhombus.
