Question

5) Show that the points (-3,2), (-5, -5), (2, -3) and (4,4) are the vertices of a rhombus.
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Answer 1

Step-by-step explanation:

let these points, A(-3,2),B(-5,-5),C(2,-3), and D(4,4)

sides are,

AB = √{(-5+3)²+(-5-2)²} = √{4+49} = √53

BC = √{(2+5)²+(-3+5)²} = √{49+4} = √53

CD = √{(4-2)²+(4+3)²} = √{4+49} = √53

AD = √{(4+3)²+(4-2)²} = √{49+4} = √53

and diagonals are,

AC = √{(2+3)²+(-3-2)²} = √{25+25} = √50

BD = √{(4+5)²+(4+5)²} = √{81+81} = √162

So,it is a rhombus because the sides are equal and diagonals are unequal

which is the property of rhombus.