Question 2 :
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 3 :
The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 
Question 4 : <br/>Let $\mathrm{P}(\mathrm{x}_{1},\mathrm{y}_{1})\mathrm{b}\mathrm{e}$ any point on the cartesian plane then match the following lists:<br/> <br/><table class="table table-bordered"><tbody><tr><td> LIST - I    </td><td> LIST - II</td></tr><tr><td> $\mathrm{A})$ The distance from $\mathrm{P}$ to X-axis</td><td>1) $0$</td></tr><tr><td> $\mathrm{B})$ The distance from $\mathrm{P}$ to Y-axis</td><td>2) $|\mathrm{y}_{1}|$</td></tr><tr><td> $\mathrm{C})$ The distance from $\mathrm{P}$ to origin is </td><td> 3) $\sqrt{x_{1}^{2}+y_{1}^{2}}$ </td></tr><tr><td> </td><td>4)$ |x_{1}|$                                   </td></tr></tbody></table>
Question 5 :
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 6 :
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 7 :
The coordinates of a point on the line y=x where perpendicular from the line 3x+4y=12 is 4 units, are
Question 8 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are
Question 9 :
The ratio in which the line joining the points $(3, 4)$ and $(5, 6)$ is divided by $x-$axis :
Question 10 :
Which of the following points is not 10 units from the origin ?
Question 11 :
Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0
Question 12 :
Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.
Question 13 :
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:<br/>
Question 14 :
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 15 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 16 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is
Question 17 :
$M(2, 6)$ is the midpoint of $\overline {AB}$. If $A$ has coordinates $(10, 12)$, the coordinates of $B$ are
Question 18 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 19 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$
Question 20 :
The coordinates of $A, B$ and $C$ are $(5, 5), (2, 1)$ and $(0, k)$ respectively. The value of $k$ that makes $\overline {AB} + \overline {BC}$ as small as possible is
Question 21 :
A rectangular hyperbola whose cente is C is cut by any circle of radius r in four point P, Q, R, S. The value of$CP^{2}+CQ^{2}+CR^{2}+CS^{2}$ is equal to :
Question 25 :
The vertices of a triangle are $(-2,0) ,(2,3)$ and  $(1, -3)$ , then the type of the triangle is 
Question 27 :
A(3 , 2) and B(5 , 4) are the end points of a line segment . Find the co-ordinates of the mid-point of the line segment .
Question 29 :
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 30 :
An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is
Question 32 :
A point R (2,-5) divides the line segment joining the point A (-3,5) and B (4,-9) , then the ratio is
Question 33 :
The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the x-axis is
Question 34 :
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)<br/>State true or false.<br/>
Question 35 :
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 36 :
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 37 :
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
Question 38 :
Slope of the line $AB$ is $-\dfrac {4}{3}$. Co-ordinates of points $A$ and $B$ are $(x, -5)$ and $(-5, 3)$ respectively. What is the value of $x$
Question 39 :
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 40 :
The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is
Question 41 :
How far is the line 3x - 4y + 15 = 0 from the origin?
Question 42 :
The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are
Question 43 :
If $A$ and $B$ are the points $(-3,4)$ and $(2,1)$, then the co-ordinates of the point $C$ on $AB$ produced such that $AC=2BC$ are 
Question 44 :
A pair of numerical coordinates is required to specify each point in a ......... plane.
Question 45 :
The line $x+y=4$ divides the line joining the points $(-1,1)$ and $(5,7)$ in the ratio
Question 46 :
Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............
Question 47 :
The points $(-2, -1), (1, 0),(4, 3),$ and $(1, 2)$ are the vertices
Question 49 :
A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.  
Question 51 :
The coordinates of one end of a diameter of a circle are $(5, -7)$. If the coordinates of the centre be $(7, 3)$, the co ordinates of the other end of the diameter are
