Question 1 :
The vertices of a triangle are $(-2,0) ,(2,3)$ and  $(1, -3)$ , then the type of the triangle is 
Question 2 :
The coordinates of $A$ and $B$ are $(1, 2) $ and $(2, 3)$. Find the coordinates of $R $, so that $A-R-B$  and   $\displaystyle \frac{AR}{RB} = \frac{4}{3}$.<br/>
Question 3 :
Which of the following points is not 10 units from the origin ?
Question 4 :
$P$ is the point $(-5,3)$ and $Q$ is the point $(-5,m)$. If the length of the straight line $PQ$ is $8$ units, then the possible value of $m$ is:
Question 5 :
The vertices P, Q, R, and S of a parallelogram are at (3,-5), (-5,-4), (7,10) and (15,9) respectively The length of the diagonal PR is
Question 6 :
A student moves $\sqrt {2x} km$ east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of $90^{\circ}$ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?
Question 7 :
Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............
Question 8 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are
Question 9 :
If $P \left( \dfrac{a}{3}, 4\right)$ is the mid-point of the line segment joining the points $Q ( 6, 5) $  and $R( 2, 3)$, then the value of $a$ is <br/>
Question 10 :
Given the points $A(-1,3)$ and $B(4,9)$.Find the co-ordinates of the mid-point of $AB$
Question 11 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$
Question 12 :
A(2,6) and B(1,7) are two vertices of a triangle ABC and the centroid is (5,7) The coordinates of C are
Question 13 :
Given the points $A(-3, 7)$ and $B(5, -9)$, determine the coordinates of point P on directed line segment that partitions in the ratio $\dfrac{1}{4}$.
Question 14 :
The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 
Question 16 :
How far is the line 3x - 4y + 15 = 0 from the origin?
Question 17 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 18 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 19 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 20 :
If a point $P\left(\displaystyle\frac{23}{5}, \frac{33}{5}\right)$ divides line AB joining two points $A(3, 5)$ and $B(x, y)$ internally in ratio of $2:3$, then the values of x and y will be.
Question 21 :
If $P(2, 2), Q(-2, 4)$ and $R(3, 4)$ are the vertices of $\Delta PQR$ then the equation of the median through vertex R is _______.
Question 22 :
Length of the median from B on AC where A (-1, 3), B (1, -1), C (5, 1) is
Question 23 :
The coordinates of the third vertex of an equilateral triangle whose two vertices are at $(3, 4), (-2 3)$ are ______.
Question 24 :
The ratio in which the line $3x+y=9$ divides the line sequent joining the points $(1,3)$ and $(2,7)$ is given by
Question 25 :
If X-axis divides the line joining $(3,-4)$ and $(5,6)$ in the ratio $a:b $, then what is the value of $\dfrac{a}{b}$?
Question 26 :
State whether the following statements are true or false . Justify your answer.<br>The points $ (0 , 5) , (0 , -9) $ and $ (3 , 6) $ are collinear .
Question 27 :
The ratio by which the line $2x + 5y - 7 = 0$ divides the straight line joining the points $(-4, 7) $ and $(6, -5)$ is
Question 28 :
State whether the following statements are true or false . Justify your answer.<br>Point $ A(-6 , 10) , B(-4 , 6) $ and $ C(3 , -8) $ are collinear such that $ AB = \dfrac{2}{9} AC $ .
Question 29 :
What is the ratio in which $P(2, 5)$ divides the line joining the points $(8, 2)$ and $(-6, 9)$?
Question 31 :
The vertices of a triangle are $A(3,4)$, $B(7,2)$ and $C(-2, -5)$. Find the length of the median through the vertex A.<br/>
Question 32 :
If $a> 0$ and $P(-a, 0), Q(a, 0)$ and $R(1,1) $ are three points such that $\displaystyle \left|(PR)^{2}-(QR)^{2} \right| = 12,$ then<br/>
Question 33 :
Determine the ratio in which the line $3x+y-9=0$ divides the line segment joining the points $(1,3)$ and $(2,7)$<br>
Question 35 :
If $\displaystyle A \left(\frac{2c}{a},\frac{c}{b}\right),B\left(\frac{c}{a},0\right)$ and $\displaystyle C\left(\frac{1+c}{a},\frac{1}{b}\right) $ are three points, then<br/>
