# CBSE Class 10-Mathematics: Chapter – 7 Coordinate Geometry Part 26 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 22:

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

(i)

(ii)

(iii)

(i)

Let

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 say that ABCD is a square.

(ii)

Let and

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

We cannot find any relation between the lengths of different sides.

Therefore, we cannot give any name to the quadrilateral ABCD.

(iii)

Let and

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

Here opposite sides of quadrilateral ABCD are equal. … (1)

We can now find out the lengths of diagonals.

Here diagonals of ABCD are not equal. … (2)

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

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