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.
Key points to solve the problem:
• The idea of distance formula- Distance between two points P(x1,y1) and Q(x2,y2) is given by- PQ =
• The idea of Rhombus – It is a quadrilateral with all four sides equal.
Given, coordinates of 4 points that form a quadrilateral as shown in fig:
Using distance formula, we have:
AB =
BC =
Clearly, AB ≠ BC ⇒ quad ABCD does not have all 4 sides equal.
∴ ABCD is not a Rhombus …ans