# The Points a (2, 0), B (9, 1), C (11, 6) and D (4, 4) Are the Vertices of a Quadrilateral Abcd. Determine Whether Abcd is a Rhombus Or Not. - Mathematics

Sum

The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

#### Solution

The given points are A (2, 0), B (9, 1), C (11, 6) and D (4, 4).
Let us find the length of all the sides of the quadrilateral ABCD.

$AB = \sqrt{\left( 2 - 9 \right)^2 + \left( 0 - 1 \right)^2} = \sqrt{50} = 5\sqrt{2}$
$BC = \sqrt{\left( 11 - 9 \right)^2 + \left( 6 - 1 \right)^2} = \sqrt{29}$
$CD = \sqrt{\left( 4 - 11 \right)^2 + \left( 4 - 6 \right)^2} = \sqrt{49 + 4} = \sqrt{53}$
$AD = \sqrt{\left( 4 - 2 \right)^2 + \left( 4 - 0 \right)^2} = \sqrt{4 + 16} = 2\sqrt{5}$
$\because AB \neq BC \neq CD \neq AD$, quadrilateral ABCD is not a rhombus.
Concept: Brief Review of Cartesian System of Rectanglar Co-ordinates
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 22 Brief review of cartesian system of rectangular co-ordinates
Exercise 22.1 | Q 4 | Page 13