Exercise 7.1

Find the distance between the following pairs of points :

(i) $(2, 3), (4, 1)$    (ii) $(-5, 7), (-1, 3)$    (iii) $(a, b), (-a, -b)$

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

Find the distance between the points $(0, 0)$ and $(36, 15)$. Can you now find the distance between the two towns $A$ and $B$ discussed in Section 7.2?

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

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

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.

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) $(4,5),\;(7,6),\;(4,3),\;(1,2)$

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

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

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 $PR$.