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

Q. Find the distance between the following pair of points:
i.) $(2,3),(4,1)$
ii.) $(-5,7),(-1.3),$
iii.) $(a,b),(-a,-b)$

Q. In a classroom, $4$ friends are seated at the points $A$, $B$, $C$ and $D$ as shown in Fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, Dont you think $ABCD$ is a square? Chameli disagrees. Using distance formula, find which of them is correct. why?

Q. 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 $PR$.

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

Q. Find the distance between the points (0 , 0) and (36 , 15) .

Q.

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

Q. To conduct Sports Day activities, in your rectangular shaped school ground $ABCD$, lines have been drawn with chalk powder at a distance of $1$ m each. $100$ flower pots have been placed at a distance of $1$m from each other along $AD$, as shown in Fig. Niharika runs $\frac{1}{4}$th the distance $AD$ on the $2$nd line and posts a green flag. Preet runs $\frac{1}{5}$th the distance $AD$ on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Q. Find the coordinates of the points which divide the line segment joining $A(-2,2)$ and $B(2,8)$ into four equal parts.

Q. Find the coordinates of a point $A$, where $AB$ is the diameter of a circle whose centre is $(2,-3)$ and $B$ is $(1,4)$.

Q. Find the ratio in which the line segment joining the points $(-3,10)$ and $(6,-8)$ is divided by $(-1,6)$.

Q. Find the coordinates of the point which divides the join of $(-1,7)$ and $(4,-3)$ in the ratio $2:3$.

Q. Find te ratio in which the line segment joining $A(1,-5)$ and $B(-4,5)$ is divided by the $x-$axis. Also find the coordinates of the point of division.

Q. Find the area of rhombus if its vertices are $(3,0),(4,5),(-1,4)$ and $(-2,-1)$ taken in order.

Q. In each of the following find the value of $k$, for which the points are collinear.
(i) $(7,-2),(5,1),(3,k)$
(ii) $(8,1),(k,-4),(2,-5)$

Q. You have studied in Class IX, that a median of a triangle divides it into two triangles of equal areas. Verify this result for $\Delta ABC$ whose vertices are $A(4,-6),B(3,-2)$ and $C(5,2)$.

Q. Find the area of the triangle whose vertices are :
(i) $(2,3),(-1,0),(2,-4)$
(ii) $(-5,-1),(3,-5),(5,2)$

Q. Find the area of the quadrilateral whose vertices taken in order, are $(-4,-2),(-3,-5),(3,-2)$ and $(2,3)$.

Q. Find a relation between $x$ and $y$ if the points $(x,y),(1,2)$ and $(7,0)$ are collinear.

Q. Determine the ratio in which the line $2x+y-4=0$ divides the line segment joining the points $A(2,-2)$ and $B(3,7)$.