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.
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