Question 1 :
The distance between the points $(a , b)$ and $(-1, -b)$ is 

Question 2 :
Find the distance between the following pair of points.<br/>$(5, 7)$ and the origin

Question 3 :
The condition for the points (x,y), (-2,2) and (3,1) to be collinear is

Question 4 :
The area of the triangle formed by the points (a,b+c), (b,c+a) and (c,a+b) is

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

Question 6 :
The slope of the line passing through the points $A(-2, 1)$ and $B(0, 3)$ is:<br/>

Question 7 :
The orthocentre of the triangle $ABC$ is $B$ and the circumstances is $S(a,b)$. If $A$ is the origin, then the coordinates of $C$ are:

Question 8 :
How far is the line 3x - 4y + 15 = 0 from the origin?

Question 9 :
The distance of the point $(x_1, y_1)$ from the origin ........

Question 11 :
The area of triangle formed by the lines $18{x}^{2}-9xy+{y}^{2}=0$ and the line $y=9$ is

Question 12 :
The vertices of a triangle ABC are A(2, 3, 1), B(-2, 2, 0) and C(0, 1, -1).Find the magnitude of the line joining mid points of the sides AC and BC.

Question 13 :
Are the points $(5,\,5),\,(8,\,2)$ and $(3,\,-4)$ are vertices of right angled triangle.

Question 14 :
A tangent to the curve $y = f(x)$ at $p(x, y)$ meets $x - axis$ at $A$ and $y-axis$ at $B$. If $\overline {AP} : \overline {BP} = 1 : 3$ and $f(1) = 1$ then the curve also passes through the point.

Question 15 :
If the straight line $ax + by + p = 0$ and $x\cos \alpha + y \sin \alpha = p$ enclosed an angle of $\dfrac {\pi}{4}$ and the line $x\sin \alpha - y \cos \alpha = 0$ meets them at the same point, then $a^{2} + b^{2}$ is

Question 16 :
If the slope of the line joining the points $ (3,4) $ and $(-2;a)$ is equal to $ - \dfrac{2}{5} , $ then the values of $a$ is equal to :

Question 17 :
The co-ordinates of the point Q$(x, y)$ which divides the line segment joining A$(-2, 1)$ and B $(1, 4)$ in the ratio $2:1$ are

Question 18 :
<b>If the slop of one of the lines represented by $ax^2-6xy+y^2=0$ is the square of the other,then the value of a is</b>

Question 19 :
The distance between $(2, 3)$ and $(-4, 5)$ is ___ .

Question 20 :
Find the slope of a line passing through the points $(-5, 2)$ and $(6, 7) $

Question 21 :
Find the slope of the line passing through the following points<br/>$M(4, 0)$ and $Q (-3, -2)$

Question 22 :
Find the coordinates of the point equidistant from the points $A(-2, -3)$, $B(-1,0)$ and $C(7,-6)$<br>

Question 23 :
The slope of the line joining $(1, 2) $ and $(1, 3)$ is ____

Question 24 :
If the length of the line AB, joining $A(4, 1)$ and $B(3, a)$ is $\sqrt{10}$, then the value of $'a'$ is

Question 25 :
A special fully automatic car is designed by the Indian scientist in the Hindustan Automobiles Ltd The car follows only the following instructions<br/>&#160;$\displaystyle G_{1}$(x) : The car shall move forward to x meters<br/>$\displaystyle G_{2}$(x) : The car shall turn in right direction and move x meters<br/>$\displaystyle G_{3}$(x) : The car shall turn in left direction and move x meters<br/>$\displaystyle G_{4}$(x) : The car shall move backward y meetrs<br/>The car is given instruction&#160;$\displaystyle G_{2}(50)$,&#160;$\displaystyle G_{3}(30)$ and&#160;$\displaystyle G_{4}(20)$ Find the shortest distance of the car from the original position. Assume that car was initially at origin and facing -ve x axis

Question 26 :
Find the slope of the line passing through the following points $P(1,-1)$&#160;and $Q (-2,5)$

Question 27 :
The area of a triangle is $5$. Two of its vertices are $(2, 1)$ &amp; $(3, -2)$. The third vertex lies on $y = x + 3$. The third vertex can be

Question 28 :
If (0, 0), (3, 0) and (x, y) are the vertices of an equilateral triangle, then the value of x and y is <br>

Question 31 :
Let ABC be a right angled triangle whose vertices are $A(0, 0), B(-8, 8)$, and $C(x, 8)$ respectively, then the possible value of x is

Question 32 :
Find the equation of the line that passes through the points $(-1,0)$ and $(-4,12)$

Question 33 :
$a, b, c$ are in A.P. and the points $A(a, 1), B(b, 2)$ and $C(c, 3)$ are such that $(OA)^{2}, (OB)^{2}$ and $(OC)^{2}$ are also in A.P; $O$ being the origin, then<br/>

Question 34 :
Area of a triangle whose vertices are (0, 0), (2, 3) , (5, 8) is ________

Question 35 :
If $(-4, 0)$ and $(1, -1)$ are two vertices of a triangle of area $4$ sq. units, then its third vertex lies on

Question 36 :
Given two points $A \equiv ( - 2,0)$ and $B \equiv (0,4)$, then find coordinate of a point $P$ lying on the line $2x-3y=9$ so that perimeter of $\Delta APB$ is least.

Question 37 :
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 38 :
The line which is parallel to x-axis and crossed the curve $\displaystyle y=\sqrt { x } $ at an angle $\displaystyle { 45 }^{ \circ }$, is<br>

Question 39 :
Area of the triangle formed by the pair of tangents drawn from(-1, 4) to $y^2 = 16x$ and the chord of contact of (-1, 4) is

Question 40 :
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 41 :
Find the slope of the line that passes through the points $(7,4)$ and $(-9,4)$

Question 42 :
$A$ is the point on the y-axis whose ordinate is $5$ and $B$ is the point $(-3, 1)$. Calculate the length of $AB$.

Question 43 :
Find the slope of the line that passes through the points $(-1,0)$ and $(3,8)$

Question 44 :
$ABC$ 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 45 :
On the line $y = 2x - 1$, what is the approximate distance between the points where $x = 1$ and $x = 2$?

Question 46 :
The points $(k, 3), (2, -4)$ and $(-k + 1, -2)$ are collinear, find $k$.

Question 47 :
If the vertices of a triangle are $(1,2),(4,-6)$ and $(3,5)$, then its area is

Question 48 :
Find the slope of the line that passes through the points $(-1,0)$ and $(3,8)$

Question 49 :
The points given are $(1, 1)$, $(-2, 7)$ and $(3, 3)$.Find distance between the points.