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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.
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.
Brief review of Cartesian System of Rectangular Coordinates | CBSE | Class 11 | Exercise 22.1 | Maths | RD Sharma
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:

According to the question, the coordinates of 4 points form a quadrilateral. This quadrilateral is shown in the below figure

Now by making use of the distance formula, we have:

RD Sharma Solutions for Class 11 Maths Chapter 22- image 10

This is pretty clear that, AB ≠ BC [This implies that quad ABCD does not have all 4 sides equal.] Therefore, ABCD can not be a Rhombus

i

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