Question 2 :
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 3 :
A line is of length $10$ m and one end is $(2,-3)$, the $x$ - co-ordinate of the other is $8$, then its $y$- coordinate is:
Question 4 :
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 5 :
Which of the following are the co-ordinates of the centre of the circle that passes through $P(6, 6), Q(3, 7)$ and $R(3, 3)$?
Question 6 :
If Q$\displaystyle \left ( \frac{a}{3},4 \right )$ is the mid-point of the line segment joining the points A(-6,5) and B(-2,3), then the value of 'a' is
Question 7 :
The point at which the two coordinate axes meet is called the
Question 8 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$
Question 10 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0
Question 11 :
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)<br/>State true or false.<br/>
Question 12 :
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 13 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 14 :
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:<br/>
Question 16 : <p>x-axis divides line segment joining points (2, -3) and (5,6) in the ratio</p>
Question 17 :
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 18 :
What will be the value of $y$ if the point $\begin{pmatrix} \dfrac { 23 }{ 5 },y \end{pmatrix}$, divides the line segment joining the points $(5,7)$ and $(4,5)$ in the ratio $2:3$ internally?<br/>
Question 19 :
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 20 :
In what ratio does the point $\begin{pmatrix} \dfrac { 1 }{ 2 },\dfrac { -3 }{ 2 } \end{pmatrix}$ divide the line segment joining the points $(3,5)$ and $(-7,9)$?<br/>
Question 21 :
Point $P$ divide a line segment $AB$ in the ratio $5:6$ where $A(0,0)$ and $B(11,0)$. Find the coordinate of the point $P$:
Question 22 :
What is the approximate slope of a line perpendicular to the line $\sqrt{11}x+\sqrt{5}y=2$?
Question 23 :
In what ratio is the line segment joining the points $(4, 6)$ and $(-7, -1)$ Is divided by $X$-axis ?
Question 25 :
Find the ratio in which the line segment joining the points $(3,5)$ and $(-4,2)$ is divided by y-axis.<br/>
Question 26 :
Select the correct option.<br>The value of $p$, for which the points $A(3,1) , B (5, p)$ and $C (7, -5)$ are collinear, is
Question 27 :
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 28 :
Let $A(-6,-5)$ and $B(-6,4)$ be two points such that a point $P$ on the line $AB$ satisfies $AP=\cfrac{2}{9}AB$. Find the point $P$.
Question 29 :
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 30 :
In how many maximum equal parts, a rectangular cake can be divided using three straight cuts?
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 :
$\mathrm{P}_{1},\ \mathrm{P}_{2},\ldots\ldots.,\ \mathrm{P}_{\mathrm{n}}$ 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 33 :
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
