Question 1 :
The coordinates of a point on the line y=x where perpendicular from the line 3x+4y=12 is 4 units, are
Question 2 :
A pair of numerical coordinates is required to specify each point in a ......... plane.
Question 3 :
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 4 :
Which of the following points is not 10 units from the origin ?
Question 5 :
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 6 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are
Question 7 :
The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the x-axis is
Question 8 :
Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0
Question 9 :
The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is
Question 11 :
The vertices of a triangle are $(-2,0) ,(2,3)$ and  $(1, -3)$ , then the type of the triangle is 
Question 12 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 13 :
Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.
Question 15 :
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 16 :
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 17 :
In what ratio, does $P(4, 6)$ divide the join of $A(-2, 3)$ and $B(6, 7)$
Question 18 :
The distance between the points $(3,5)$ and $(x,8)$ is $5$ units. Then the value of $x$ 
Question 19 :
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 20 :
Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.
Question 21 :
The point at which the two coordinate axes meet is called the
Question 22 :
The line $x+y=4$ divides the line joining the points $(-1,1)$ and $(5,7)$ in the ratio
Question 23 :
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 24 :
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 25 :
If a point $C$ be the mid-point of a line segment $AB$, then $AC = BC = (...) AB$.
Question 26 :
The distance between the points (sin x, cos x) and (cos x -sin x) is
Question 27 : <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 28 :
An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is
Question 29 :
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)<br/>State true or false.<br/>
Question 30 :
Given the points $A(-1,3)$ and $B(4,9)$.Find the co-ordinates of the mid-point of $AB$
Question 31 :
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 32 :
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 33 :
The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are
Question 34 :
How far is the line 3x - 4y + 15 = 0 from the origin?
Question 35 :
If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length
Question 36 :
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 37 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$
Question 38 :
Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............
Question 40 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0
Question 41 :
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 42 :
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 43 :
A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.  
Question 45 :
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 47 :
The point which lies in the perpendicular bisector of the line segment joining the points A (-2, -5) and B (2,5) is
Question 49 :
If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=
Question 50 :
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 51 :
The point which lies on the perpendicular bisector of the line segment joining the points $P(-2,0)$ and $Q(2,5)$ is:
Question 52 :
The coordinate of point which divides the line segment joining points $A(0,0)$ and $B(9,12)$ in the ratio $1:2$, are
Question 53 :
The line joining $(5, 0)$ to $(10\cos\theta, 10\sin\theta)$ is divided internally in the ratio $2:3$ at $P$, then the locus of $P$ is
Question 54 :
The point which divides the line segmentjoining the points (3, 5) and (8, 10) internallyin the ratio 2 :3 is:
Question 55 :
The ratio in which X-axis divides the line segment joining $(3,6)$ and $(12,-3)$ is
Question 56 :
The ratio in which the joint of (-3, 10), (6, -8)is divided by (-1, 6),
Question 57 :
In what ratio does the point P(-2, 3) divide theline segment joining the points A(-3, 5) andB(4, -9) internally?
Question 58 :
There are two point $P(1,-4)$ and $Q(4,2)$. Find a point X dividing the line PQ in the ratio $1:2$
Question 59 :
The mid-point of line segment joining thepoints (3, 0) and (-1, 4) is :
Question 60 :
The point P divides the line segment joining the points $\displaystyle A\left ( 2,1 \right )$ and $\displaystyle B\left ( 5,-8\right )$ such that $ \frac{AP}{AB}=\frac{1}{3}$ If P lies on the line $\displaystyle 2x+y+k=0$<br/>then the value of k is-
Question 61 :
The points $A$ $(x_1, y_1), B (x_2, y_2)$ and $C (x_3, y_3)$ are the vertices of $\Delta $ ABC.<br/>The median $AD$ meets $BC$ at $D$.<br/>Find the coordinates of points Q and R on medians BE and CF, respectively such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.<br/>
Question 62 :
The ratio in which the line $3x+y-9=0$ divides the line segment joining points (1, 3) and (2, 7) is:
Question 63 :
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 64 :
Find the coordinates of the point $P$ which divides line segment $QR$ internally in the ratio $m:n$ in the following example:<br/>$Q \equiv (6, -5), R \equiv (-10, 2)$ and $m:n = 3:4$
Question 65 :
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 66 :
Find the ratio in which the line segment joining the points $(3,5)$ and $(-4,2)$ is divided by y-axis.<br/>
Question 67 :
What is the ratio in which $P(2, 5)$ divides the line joining the points $(8, 2)$ and $(-6, 9)$?
Question 68 :
What is the approximate slope of a line perpendicular to the line $\sqrt{11}x+\sqrt{5}y=2$?
Question 69 : <p>x-axis divides line segment joining points (2, -3) and (5,6) in the ratio</p>
Question 70 :
The ratio by which the line $2x + 5y - 7 = 0$ divides the straight line joining the points $(-4, 7) $ and $(6, -5)$ is
Question 71 :
The straight line $3x+y=9$ divides the line segment joining the points $(1,\,3)$ and $(2,\,7)$ in the ratio
Question 72 :
If the line joining A(2, 3) and B(-5, 7) is cut by X - axis at P, then find AP : PB.
Question 73 :
If the line $2x+y=k$ passes through the point which divides the line segment joining the point $(1,1)$ & $(2,4)$ in the ratio $3:2$ then $k$ equal
Question 74 :
If the point P (2, 1) lies on the segment joining Points A (4, 2) and B (8, 4) then
Question 75 :
Length of the median from B on AC where A (-1, 3), B (1, -1), C (5, 1) is
Question 76 :
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
Question 77 :
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 78 :
The coordinates of the point which divides the line segment joining the points $(-7, 4)$ and $(-6, -5)$ internally in the ratio $7 : 2$ is:
Question 79 :
Find the coordinates of the point which divides the line segment joining $(-3,5)$ and $(4,-9)$ in the ratio $1:6$ internally.
Question 80 :
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 81 :
Find the midpoint of the segment joining the points $(4, -2)$ and $(-8,6)$.
Question 82 :
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 83 :
In what ratio is the line segment joining the points $(4, 6)$ and $(-7, -1)$ Is divided by $X$-axis ?
Question 84 :
<i></i>If the coordinates of opposite vertices of a square are $(1,3)$ and $(6,0)$, the length if a side od a square is 
Question 85 :
Find the distance between the points $(-1,-3)$ and the midpoint of the line segment joining $(2,4)$ and $(4,6)$.
Question 86 :
$A(5,1)$, $B(1,5)$ and $C(-3, -1)$ are the vertices of $\Delta ABC$. The length of its median AD is:
Question 87 :
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 88 :
If the point $(x_1 + t (x_2 -x_1), y_1+t (y_2-y_1))$ divides the join of $(x_1, y_1)$ and $(x_2, y_2)$ internally, then
Question 89 :
The point which is equi-distant from the points $(0,0),(0,8) and (4,6)$ is 
Question 90 :
If P(x, y) is any point on the line joining thepoints (a, 0) and (0, b) then the value of$\displaystyle \frac{x}{a} + \frac{y}{b}$
Question 91 :
The line segment joining the points $(3, -4)$ and $(1, 2) $ is trisected at the points P and Q. If the and co-ordinates of P and Q are $(p, -2)$ and $(\frac{5}{3}, q)$ respectively, find the value of p and q.
Question 92 :
In how many maximum equal parts, a rectangular cake can be divided using three straight cuts?
Question 93 :
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 94 :
If we take $11$ points on a ray which is drawn at acute angle to a line segment, then the line segment can be divided into maximum _____ equal points.
Question 95 :
The coordinates of the third vertex of an equilateral triangle whose two vertices are at $(3, 4), (-2 3)$ are ______.
Question 97 :
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 98 :
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 99 :
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 100 :
Number of points with integral co-ordinates that lie inside a triangle whose co-ordinate are (0,0), (0, 21) and (21, 0)
Question 101 :
If $(-6, -4), (3, 5), (-2, 1)$ are the vertices of a parallelogram, then remaining vertex can be
Question 102 :
If $P \left( \dfrac{a}{3},\dfrac{b}{2} \right)$ is the mid-point of the line segment joining $A(-4,3)$ and $B(-2,4)$ then $(a,b)$ is 
Question 103 :
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 105 :
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 106 :
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 107 :
The points $(-2,2)$, $(8, -2)$ and $(-4, -3)$ are the vertices of a:
Question 108 :
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 109 :
$ABC$ is an isosceles triangle. If the coordinates of the base are $B(1,3)$ and $C(-2,7)$. The vertex $A$ can be
Question 110 :
If a line intercepted between the coordinate axes is trisected at a point $A(4, 3),$ which is nearer to $x-$axis, then its equation is
Question 111 :
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 112 :
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 113 :
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 114 :
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 115 :
The points given are $(1, 1)$, $(-2, 7)$ and $(3, 3)$.Find distance between the points.
Question 116 :
$\mathrm{P}_{1},\ \mathrm{P}_{2},\ldots\ldots.,\ \mathrm{P}_{\mathrm{n}}$ 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 117 :
The mid point of the segment joining $(2a, 4)$ and $(-2, 2b)$ is $(1, 2a+1)$, then value of b is
Question 118 :
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 119 :
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.
Question 120 :
Consider the points $A(0,\ 1)$ and $B(2,\ 0)$, and $P$ be a point on the line $4x+3y+9=0$. The coordinates of $P$ such that $|PA-PB|$ is maximum are
Question 121 :
$ABC$ 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 122 :
Find the ratio in  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 123 :
The point whose abscissa is equal to its ordinate and which is equidistant from $A(5,0)$ and $B(0,3)$ is
Question 124 :
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 125 :
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 126 :
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 127 :
If $\displaystyle(-1,2),(2,-1)$ and $\displaystyle(3,1)$ are any three vertices of a parallelogram then the fourth vertex $\displaystyle(a,b)$ will be such that
