Option 4 : None

Cell

345924

10 Questions
10 Marks
7 Mins

**Given:**

A (x_{1}, y_{1}) = (4, 3), B (x_{2}, y_{2}) = (6, 2), C (x_{3}, y_{3}) = (7, 4) and D (x_{4}, y_{4}) = (3, 1)

**Concept:**

Use of distance formula for finding the type of quadrilateral.

**Formula used:**

Distance AB = \(\sqrt {{\rm{(x2\;-\;x1)2\; + \;(y2\;-\;y1)2\;}}}\)

⇒ AB = \(\sqrt {{\rm{(6\;-\;4)2\; + \;(2\;-\;3)2\;}}}\)

⇒ AB = √5

Distance BC = \(\sqrt {{\rm{(x3\;-\;x2)2\; + \;(y3\;-\;y2)2\;}}}\)

⇒ BC = \(\sqrt {{\rm{(7\;-\;6)2\; + \;(4\;-\;2)2\;}}}\)

⇒ BC = √5

Distance CD = \(\sqrt {{\rm{(x4\;-\;x3)2\; + \;(y4\;-\;y3)2\;}}}\)

⇒ CD = \(\sqrt {{\rm{(3\;-\;7)2\; + \;(1\;-\;4)2\;}}}\)

⇒ CD = 5

Distance DA = \(\sqrt {{\rm{(x4\;-\;x1)2\; + \;(y4\;-\;y1)2\;}}}\)

⇒ DA = \(\sqrt {{\rm{(3\;-\;4)2\; + \;(1\;-\;3)2\;}}}\)

⇒ DA = √5

From the above result we can see that three sides of the quadrilateral are equal but fourth one is not equal.