Q6 of 53 Page 107

Show that points A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are vertices of a rhombus ABCD.

In a Rhombus the sides are equal and the diagonals bisect each other at 90°

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
 .....(1)


Length AB = =


Length BC = =


Length CD = =


Length AD = =


Slope of a line between two points (a,b) and (c,d) is



Slope of Diagonal AC = = 1


Slope of diagonal BD = = -1


Note: If the Product of slopes of two lines = -1 then they are perpendicular to each other.


As the product of slopes pf two diagonals = -1. Hence they're perpendicular to each other.


Hence The given points form a rhombus.


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