Question 1 :
If $(-6, -4), (3, 5), (-2, 1)$ are the vertices of a parallelogram, then remaining vertex can be

Question 2 :
If the three distance points $\left( { t }_{ i\quad }2{ at }_{ i }+{ { at }^{ 3 }_{ i } } \right) \quad for\quad i=1,2,3$ are collinear then the sum of the abscissae of the points is

Question 3 :
The points $A\left( {2a,\,4a} \right),\,B\left( {2a,\,6a} \right)\,$ and $C\left( {2a + \sqrt 3 a,\,5a} \right)$ (when $a>0$) are vertices of 

Question 4 :
$ABC$ is an isosceles triangle. If the coordinates of the base are $B(1,3)$ and $C(-2,7)$. The vertex $A$ can be

Question 5 :
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 6 :
$ABC$ is an equilateral triangle. If the coordinates of two of its vertices are ($1, 3)$ and $(-2, 7)$ the coordinates of the third vertex can be<br>

Question 7 :
If the line $2x+y=k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ in the ratio $3 : 2$ ,then $k$ equals:

Question 8 :
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 9 :
Find the ratio in &#160;which the point $P(2,y)$ divides the line segment joining the point $A(-2,2)$ and $B(3,7)$. Also find the value of $y$.<br/>

Question 10 :
If the coordinates of the extermities of diagonal of a square are $(2,-1)$ and $(6,2)$, then the coordinates of extremities of other diagonal are

Question 11 :
If $P \left( \dfrac{a}{3},\dfrac{b}{2}&#160;\right)$ is the mid-point of the line segment joining $A(-4,3)$ and $B(-2,4)$ then $(a,b)$ is&#160;

Question 12 :
Find the point on the x-axis which is equidistant from the points $(-2,5)$ and $(2, -3)$. Hence find the area of the triangle formed by these points<br>

Question 13 :
If two vertices of a parellelogram are $(3,2)$ and $(-1,0)$ and the diagonals intersect at $(2, -5)$, then the other two vertices are:

Question 14 :
Three points $\left( {0,0} \right),\left( {3,\sqrt 3 } \right),\left( {3,\lambda } \right)$ from an equilateral triangle, then $\lambda $ is equal to

Question 15 :
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/>

Question 16 :
The points $(-2,2)$, $(8, -2)$ and $(-4, -3)$ are the vertices of a:

Question 17 :
If $P\left( x,y,z \right) $ is a point on the line segment joining $Q\left( 2,2,4 \right) $ and $R\left( 3,5,6 \right) $ such that the projections of $OP$ on the axis are $\cfrac { 13 }{ 5 } ,\cfrac { 19 }{ 5 } ,\cfrac { 26 }{ 5 } $ respectively, then $P$ divides $QR$ in the ratio

Question 18 :
$\mathrm{P}_{1},\ \mathrm{P}_{2},\ldots\ldots.,\ \mathrm{P}_{\mathrm{n}}$ are points on the line $y=x$ lying in the positive quadrant such that $\mathrm{O}\mathrm{P}_{\mathrm{n}}=n\cdot\mathrm{O}\mathrm{P}_{\mathrm{n}-1}$, where $\mathrm{O}$ is the origin. If $\mathrm{O}\mathrm{P}_1=1$ and the coordinates of $\mathrm{P}_{\mathrm{n}}$ are $(2520\sqrt{2},2520\sqrt{2})$, then $n$ is equal to<br/>

Question 19 :
The mid point of the segment joining $(2a, 4)$ and $(-2, 2b)$ is $(1, 2a+1)$, then value of b is

Question 20 :
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 PQ.