A(-3;2),B(2;3),C(1;-2),D(-4;-3) show that ABCD is a rhombus
A rhombus has 4 equal sides, in 2 pairs of parallel sides.
AB = √(25+1) = √26
BC = √(1+25) = √26
CD = √(25+1) = √26
DA = √(1+25) = √26
so, all sides equal
AB has slope 1/5
BC has slope -5/-1 = 5
CD has slope -1/-5 = 1/5
DA has slope -5/-1 = 5
slopes match up.
We gotta rhombus.