**Distance Formula CBSE NCERT solutions Chapter 7 Exercise 7.1 Question 6**

**6.** Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.

**(i) (-1, -2), (1, 0), (-1, 2), (-3, 0)**

**(ii) (-3, 5), (3, 1), (0, 3) , (-1, -4)**

**(iii) (4, 5), (7, 6), (4, 3), (1, 2)**

**Solution (i)**

Let **A = (-1, -2), B = (1, 0), C= (-1, 2) and D = (-3, 0)**

Using **Distance Formula** to find distances **AB, BC, CD and DA,** we get

Therefore,** all four sides of quadrilateral are equal. (1)**

Now, we will check the length of diagonals.

Therefore, **diagonals of quadrilateral ABCD are also equal.** ** (2)**

From **(1)** and **(2)**, we can definitely say that **ABCD is a square.**

**Solution (ii)**

Let **A =** **(-3, 5), B= (3, 1), C= (0, 3) and D= (-1, -4)**

Using **Distance Formula** to find distances **AB, BC, CD and DA,** we get

**We cannot find any relation between the length of different sides. Therefore, we cannot give any name to the quadrilateral ABCD.**

**Solution (iii)**

**Let A = (4, 5), B= (7, 6), C= (4, 3) and D= (1, 2)**

Using **Distance Formula** to find distances **AB, BC, CD and DA,** we get

**We can note that opposite sides of quadrilateral ABCD are equal. (1)**

**We can now find out the lengths of diagonals.**

We can see that **diagonals of ABCD are not equal**. **(2)**

**From (1) and (2), **we can say that **ABCD** is not a rectangle we can just write it a **parallelogram**.