Q. 195.0( 1 Vote )

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Answer :

Given: Points ( - 3, 2), ( - 5, - 5), (2, - 3) and (4, 4).


To find: Area of a rhombus.


Formula Used:


The distance between the points (x1,y1) and (x2,y2) is:


Distance


Area of the triangle having vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃)
= 1/2 |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |


Explanation:



Vertices of the rhombus are: A ( - 3, 2), B( - 5, - 5), C(2, - 3) and D(4, 4)


We know that diagonals of a rhombus bisect each other. Therefore the point of intersection of diagonals is:


The abscissa of Midpoint of AC =


Ordinate of Midpoint of AC =


The abscissa of Midpoint of BD =


The ordinate of Midpoint of BD =


Since the diagonals AC and BD bisect each other at O. Therefore it is a rhombus.


Length of diagonal AC = units


Length of diagonal BD = units


Area of rhombus = = 45 sq units


Area of rhombus is 45 sq units


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