In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

                                                        

 

Find a relation between $x$ and $y$ such that the point ($x$, $y$) is equidistant from the point (3, 6) and (– 3, 4).

Find the distance between the following pairs of points : (iii) ($a$, $b$), (– $a$, – $b$)

If Q(0, 1) is equidistant from P(5, –3) and R($x$, 6), find the values of $x$. Also find the distances QR and PR.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (iii) (4, 5), (7, 6), (4, 3), (1, 2)

Find the values of $y$ for which the distance between the points P(2, – 3) and Q(10, $y$) is 10 units.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)

Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

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)

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

Find the distance between the following pairs of points : (i) (2, 3), (4, 1)

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B.

Find the distance between the following pairs of points : (ii) (– 5, 7), (– 1, 3)