Question 1 :
The points which trisect the line segment joining the points $(0,0)$ and $(9,12)$ are

Question 2 :
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 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 5 :
The point at which the two coordinate axes meet is called the

Question 6 :
The coordinates of the midpointof a line segment joining$P ( 5,7 )$ and Q $( - 3,3 )$ are

Question 7 :
If A(x,0), B(-4,6), and C(14, -2) form an isosceles triangle with AB=AC, then x=

Question 8 :
The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is

Question 9 :
Find the distance from the point (2, 3) to the line 3x + 4y + 9 = 0

Question 10 :
The point which lies in the perpendicular bisector of the line segment joining the points A (-2, -5) and B (2,5) is

Question 11 :
Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0

Question 12 :
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 13 :
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 14 :
$A=\left(2,-1\right), B=\left(4,3\right)$. If $AB$ is extended to $C$ such that $AB=BC$, then $C=$

Question 15 :
The centroid of the triangle with vertices (2,6), (-5,6) and (9,3) is

Question 16 :
$P$ 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 17 :
If the distance between the points $(4, p)$ and $(1, 0)$ is $5$, then the value of $p$ is:<br/>

Question 18 :
How far is the line 3x - 4y + 15 = 0 from the origin?

Question 19 :
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 20 :
Find the value of $x$ if the distance between the points $(2, -11)$ and $(x, -3)$ is $10$ units.

Question 21 :
Distance between the points $(2,-3)$ and $(5,a)$ is $5$. Hence the value of $a=$............

Question 22 :
The vertices of a triangle are $(-2,0) ,(2,3)$ and&#160; $(1, -3)$ , then the type of the triangle is&#160;

Question 23 :
The distance between the points (sin x, cos x) and (cos x -sin x) is

Question 24 :
A pair of numerical coordinates is required to specify each point in a ......... plane.

Question 25 :
Which of the following points is not 10 units from the origin ?

Question 26 :
<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/>&#160;<br/><table class="table table-bordered"><tbody><tr><td>&#160;LIST - I &#160; &#160;</td><td>&#160;LIST - II</td></tr><tr><td>&#160;$\mathrm{A})$ The distance from&#160;$\mathrm{P}$ to X-axis</td><td>1) $0$</td></tr><tr><td>&#160;$\mathrm{B})$ The distance from&#160;$\mathrm{P}$ to Y-axis</td><td>2) $|\mathrm{y}_{1}|$</td></tr><tr><td>&#160;$\mathrm{C})$ The distance from&#160;$\mathrm{P}$ to origin is&#160;</td><td>&#160;3) $\sqrt{x_{1}^{2}+y_{1}^{2}}$&#160;</td></tr><tr><td>&#160;</td><td>4)$ |x_{1}|$&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;</td></tr></tbody></table>

Question 28 :
$M(2, 6)$ is the midpoint of $\overline {AB}$. If $A$ has coordinates $(10, 12)$, the coordinates of $B$ are

Question 29 :
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 30 :
The ratio in which the line joining the points $(3, 4)$ and $(5, 6)$ is divided by $x-$axis :

Question 31 :
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 32 :
Given the points $A(-1,3)$ and $B(4,9)$.Find the co-ordinates of the mid-point of $AB$

Question 33 :
If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length

Question 34 :
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 35 :
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 36 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?

Question 37 :
An isosceles triangle has vertices at (4,0), (-4,0), and (0,8) The length of the equal sides is

Question 38 :
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&#160;

Question 39 :
A point R (2,-5) divides the line segment joining the point A (-3,5) and B (4,-9) , then the ratio is

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 :
The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)<br/>State true or false.<br/>

Question 43 :
The coordinates of $A$ and $B$ are $(1, 2) $ and $(2, 3)$. Find the coordinates of $R $, so that $A-R-B$&#160; and&#160; &#160;$\displaystyle \frac{AR}{RB} = \frac{4}{3}$.<br/>

Question 44 :
Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.

Question 45 :
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 46 :
The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the x-axis is

Question 47 :
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 49 :
The points $(-2, -1), (1, 0),(4, 3),$ and $(1, 2)$ are the vertices

Question 50 :
A Cartesian plane consists of two mutually _____ lines intersecting at their zeros. &#160;