Show that the quadrilateral whose vertices are (2,-1),(3,4),(-2,3),(-3,-2) is a rhombus

Show that the quadrilateral whose vertices are (2,-1),(3,4),(-2,3),(-3

1.	Show that the quadrilateral whose vertices are (2,-1),(3,4),(-2,3),(-3,-2) is a rhombus
Answer» Let A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2){tex}A B = \\sqrt { ( 3 - 2 ) ^ { 2 } + ( 4 + 1 ) ^ { 2 } } = \\sqrt { ( 1 ) ^ { 2 } + ( 5 ) ^ { 2 } } = \\sqrt { 1 + 25 } = \\sqrt { 26 }{/tex}{tex}B C = \\sqrt { ( - 2 - 3 ) ^ { 2 } + ( 3 - 4 ) ^ { 2 } } = \\sqrt { ( - 5 ) ^ { 2 } + ( - 1 ) ^ { 2 } } = \\sqrt { 25 + 1 } = \\sqrt { 26 }{/tex}{tex}C D = \\sqrt { ( - 3 + 2 ) ^ { 2 } + ( - 2 - 3 ) ^ { 2 } } = \\sqrt { ( - 1 ) ^ { 2 } + ( - 5 ) ^ { 2 } } = \\sqrt { 1 + 25 } = \\sqrt { 26 }{/tex}{tex}A D = \\sqrt { ( - 3 - 2 ) ^ { 2 } + ( - 2 + 1 ) ^ { 2 } } = \\sqrt { ( - 5 ) ^ { 2 } + ( - 1 ) ^ { 2 } } = \\sqrt { 25 + 1 } = \\sqrt { 26 }{/tex}Since AB = BC = CD = AD{tex}\\therefore{/tex}ABCD is a rhombus.