Question 1:
Find the slope of the line through the points $(3,-2)$ and $(-1, 4)$.
Question 2:
Find the slope of the line through the points $(3,-2)$ and $(7,-2)$.
Question 3:
Find the slope of the line through the points $(3, -2)$ and $(3, 4)$.
Question 4:
Find the slope of the line whose inclination is $\alpha=60^{\circ}$.
Question 5:
If the angle between two lines is $\frac{\pi}{4}$ and slope of one of the lines is $\frac{1}{2}$, find the slope of the other line.
Question 6:
Line through the points $(-2, 6)$ and $(4, 8)$ is perpendicular to the line through the points $(8, 12)$ and $(x, 24)$. Find the value of $x$.
Question 7:
Find the equations of the lines parallel to axes and passing through $(-2, 3)$.
Question 8:
Find the equation of the line through $(-2, 3)$ with slope $-4$.
Question 9:
Write the equation of the line through the points $(1, -1)$ and $(3, 5)$.
Question 10:
Write the equation of the line for which $\tan \theta = \frac{1}{2}$ and $y$-intercept is $-\frac{3}{2}$.
Question 11:
Write the equation of the line for which $\tan \theta = \frac{1}{2}$ and $x$-intercept is $4$.
Question 12:
Find the equation of the line, which makes intercepts $-3$ and $2$ on the $x$- and $y$-axes respectively.
Question 13:
Find the distance of the point $(3,-5)$ from the line $3x-4y-26=0$.
Question 14:
Find the distance between the parallel lines $3x-4y+7=0$ and $3x-4y+5=0$.
Question 15:
If the lines $2x+y-3=0$, $5x+ky-3=0$ and $3x-y-2=0$ are concurrent, find the value of $k$.
Question 16:
Find the distance of the line $4x-y=0$ from the point $P(4,1)$ measured along the line making an angle of $135^{\circ}$ with the positive $x$-axis.
Question 17:
Assuming that straight lines work as the plane mirror for a point, find the image of the point $(1, 2)$ in the line $x-3y+4=0$.
Question 18:
Show that the area of the triangle formed by the lines $y=m_1x+c_1$, $y=m_2x+c_2$ and $x=0$ is $\frac{(c_1-c_2)^{2}}{2|m_1-m_2|}$.
Question 19:
A line is such that its segment between the lines $5x-y+4=0$ and $3x+4y-4=0$ is bisected at the point $(1, 5)$. Obtain its equation.
Question 20:
Show that the path of a moving point such that its distances from two lines $3x-2y=5$ and $3x+2y=5$ are equal is a straight line.
Question 21:
Draw a quadrilateral in the Cartesian plane, whose vertices are $(-4, 5)$, $(0, 7)$, $(5,-5)$ and $(-4,-2)$.
Question 22:
The base of an equilateral triangle with side $2a$ lies along the $y$-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.
Question 23:
Find the distance between $P(x_1,y_1)$ and $Q(x_2,y_2)$ when $PQ$ is parallel to the $y$-axis.
Question 24:
Find the distance between $P(x_1,y_1)$ and $Q(x_2,y_2)$ when $PQ$ is parallel to the $x$-axis.
Question 25:
Find a point on the $x$-axis, which is equidistant from the points $(7, 6)$ and $(3, 4)$.
Question 26:
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points $P(0,-4)$ and $B (8, 0)$.
Question 27:
Without using the Pythagoras theorem, show that the points $(4, 4)$, $(3, 5)$ and $(-1,-1)$ are the vertices of a right angled triangle.
Question 28:
Find the slope of the line, which makes an angle of $30^{\circ}$ with the positive direction of $y$-axis measured anticlockwise.
Question 29:
Without using distance formula, show that points $(-2,-1)$, $(4,0)$, $(3,3)$ and $(-3,2)$ are the vertices of a parallelogram.
Question 30:
Find the angle between the $x$-axis and the line joining the points $(3,-1)$ and $(4,-2)$.
Question 31:
The slope of a line is double of the slope of another line. If tangent of the angle between them is $\frac{1}{3}$, find the slopes of the lines.
Question 32:
A line passes through $(x_1,y_1)$ and $(h,k)$. If slope of the line is $m$, show that $k-y_1=m(h-x_1)$.
Question 33:
Write the equations for the $x$-and $y$-axes.
Question 34:
Find the equation of the line passing through the point $(-4,3)$ with slope $\frac{1}{2}$.
Question 35:
Find the equation of the line passing through $(0, 0)$ with slope $m$.
Question 36:
Find the equation of the line passing through $(2,2\sqrt{3})$ and inclined with the $x$-axis at an angle of $75^{\circ}$.
Question 37:
Find the equation of the line intersecting the $x$-axis at a distance of $3$ units to the left of origin with slope $-2$.
Question 38:
Find the equation of the line intersecting the $y$-axis at a distance of $2$ units above the origin and making an angle of $30^{\circ}$ with positive direction of the $x$-axis.
Question 39:
Find the equation of the line passing through the points $(-1, 1)$ and $(2,-4)$.
Question 40:
The vertices of $\triangle PQR$ are $P(2,1)$, $Q(-2,3)$ and $R(4,5)$. Find equation of the median through the vertex $R$.
Question 41:
Find the equation of the line passing through $(-3, 5)$ and perpendicular to the line through the points $(2, 5)$ and $(-3, 6)$.
Question 42:
A line perpendicular to the line segment joining the points $(1, 0)$ and $(2, 3)$ divides it in the ratio $1: n$. Find the equation of the line.
Question 43:
Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2, 3)$.
Question 44:
Find equation of the line passing through the point $(2, 2)$ and cutting off intercepts on the axes whose sum is $9$.
Question 45:
Find equation of the line through the point $(0, 2)$ making an angle $\frac{2\pi}{3}$ with the positive $x$-axis. Also, find the equation of line parallel to it and crossing the $y$-axis at a distance of $2$ units below the origin.
Question 46:
The perpendicular from the origin to a line meets it at the point $(-2,9)$, find the equation of the line.
Question 47:
The length $L$ (in centimetre) of a copper rod is a linear function of its Celsius temperature $C$. In an experiment, if $L=124.942$ when $C=20$ and $L=125.134$ when $C=110$, express $L$ in terms of $C$.
Question 48:
The owner of a milk store finds that, he can sell $980$ litres of milk each week at $\mathrm{Rs}$ $14/\text{litre}$ and $1220$ litres of milk each week at $\mathrm{Rs}$ $16/\text{litre}$. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at $\mathrm{Rs}$ $17/\text{litre}$?
Question 49:
$P(a,b)$ is the mid-point of a line segment between axes. Show that equation of the line is $\frac{x}{a}+\frac{y}{b}=2$.
Question 50:
Point $R (h,k)$ divides a line segment between the axes in the ratio $1: 2$. Find equation of the line.
Question 51:
By using the concept of equation of a line, prove that the three points $(3, 0)$, $(-2,-2)$ and $(8, 2)$ are collinear.
Question 52:
Reduce the equation $x+7y=0$ into slope - intercept form and find its slope and the $y$-intercept.
Question 53:
Reduce the equation $6x+3y-5=0$ into slope - intercept form and find its slope and the $y$-intercept.
Question 54:
Reduce the equation $y=0$ into slope - intercept form and find its slope and the $y$-intercept.
Question 55:
Reduce the equation $3x+2y-12=0$ into intercept form and find its intercepts on the axes.
Question 56:
Reduce the equation $4x-3y=6$ into intercept form and find its intercepts on the axes.
Question 57:
Reduce the equation $3y+2=0$ into intercept form and find its intercepts on the axes.
Question 58:
Find the distance of the point $(-1,1)$ from the line $12(x+6)=5(y-2)$.
Question 59:
Find the points on the $x$-axis, whose distances from the line $\frac{x}{3}+\frac{y}{4}=1$ are $4$ units.
Question 60:
Find the distance between parallel lines $15x+8y-34=0$ and $15x+8y+31=0$.
Question 61:
Find the distance between parallel lines $l(x+y)+p=0$ and $l(x+y)-r=0$.
Question 62:
Find equation of the line parallel to the line $3x-4y+2=0$ and passing through the point $(-2, 3)$.
Question 63:
Find equation of the line perpendicular to the line $x-7y+5=0$ and having $x$ intercept $3$.
Question 64:
Find angles between the lines $\sqrt{3}x+y=1$ and $x+\sqrt{3}y=1$.
Question 65:
The line through the points $(h,3)$ and $(4,1)$ intersects the line $7x-9y-19=0$ at right angle. Find the value of $h$.
Question 66:
Prove that the line through the point $(x_1,y_1)$ and parallel to the line $Ax+By+C=0$ is $A(x-x_1)+B(y-y_1)=0$.
Question 67:
Two lines passing through the point $(2,3)$ intersects each other at an angle of $60^{\circ}$. If slope of one line is $2$, find equation of the other line.
Question 68:
Find the equation of the right bisector of the line segment joining the points $(3,4)$ and $(-1,2)$.
Question 69:
Find the coordinates of the foot of perpendicular from the point $(-1,3)$ to the line $3x-4y-16=0$.
Question 70:
The perpendicular from the origin to the line $y=mx+c$ meets it at the point $(-1,2)$. Find the values of $m$ and $c$.
Question 71:
If $p$ and $q$ are the lengths of perpendiculars from the origin to the lines $x \cos \theta - y \sin \theta = k \cos 2\theta$ and $x \sec \theta + y \csc \theta = k$, respectively, prove that $p^2+4q^2=k^2$.
Question 72:
In the triangle $ABC$ with vertices $A(2,3)$, $B(4,-1)$ and $C(1,2)$, find the equation and length of altitude from the vertex $A$.
Question 73:
If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$, then show that $\frac{1}{p^{2}}=\frac{1}{a^{2}}+\frac{1}{b^{2}}$.
Question 74:
Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is parallel to the $x$-axis.
Question 75:
Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is parallel to the $y$-axis.
Question 76:
Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is passing through the origin.
Question 77:
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are $1$ and $-6$, respectively.
Question 78:
What are the points on the $y$-axis whose distance from the line $\frac{x}{3}+\frac{y}{4}=1$ is $4$ units.
Question 79:
Find perpendicular distance from the origin to the line joining the points $(\cos \theta, \sin \theta)$ and $(\cos \phi, \sin \phi)$.
Question 80:
Find the equation of the line parallel to $y$-axis and drawn through the point of intersection of the lines $x-7y+5=0$ and $3x+y=0$.
Question 81:
Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point, where it meets the $y$-axis.
Question 82:
Find the area of the triangle formed by the lines $y-x=0$, $x+y=0$ and $x-k=0$.
Question 83:
Find the value of $p$ so that the three lines $3x+y-2=0$, $px+2y-3=0$ and $2x-y-3=0$ may intersect at one point.
Question 84:
If three lines whose equations are $y=m_1x+c_1$, $y=m_2x+c_2$ and $y=m_3x+c_3$ are concurrent, then show that $m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0$.
Question 85:
Find the equation of the lines through the point $(3,2)$ which make an angle of $45^{\circ}$ with the line $x-2y=3$.
Question 86:
Find the equation of the line passing through the point of intersection of the lines $4x+7y-3=0$ and $2x-3y+1=0$ that has equal intercepts on the axes.
Question 87:
Show that the equation of the line passing through the origin and making an angle $\theta$ with the line $y=mx+c$ is $\frac{y}{x}=\frac{m \pm \tan \theta}{1 \mp m \tan \theta}$.
Question 88:
In what ratio, the line joining $(-1,1)$ and $(5,7)$ is divided by the line $x+y=4$?
Question 89:
Find the distance of the line $4x+7y+5=0$ from the point $(1,2)$ along the line $2x-y=0$.
Question 90:
Find the direction in which a straight line must be drawn through the point $(-1,2)$ so that its point of intersection with the line $x+y=4$ may be at a distance of $3$ units from this point.
Question 91:
The hypotenuse of a right angled triangle has its ends at the points $(1,3)$ and $(-4,1)$. Find an equation of the legs (perpendicular sides) of the triangle which are parallel to the axes.
Question 92:
Find the image of the point $(3,8)$ with respect to the line $x+3y=7$ assuming the line to be a plane mirror.
Question 93:
If the lines $y=3x+1$ and $2y=x+3$ are equally inclined to the line $y=mx+4$ find the value of $m$.
Question 94:
If sum of the perpendicular distances of a variable point $P(x,y)$ from the lines $x+y-5=0$ and $3x-2y+7=0$ is always $10$. Show that $P$ must move on a line.
Question 95:
Find equation of the line which is equidistant from parallel lines $9x+6y-7=0$ and $3x+2y+6=0$.
Question 96:
A ray of light passing through the point $(1, 2)$ reflects on the $x$-axis at point $A$ and the reflected ray passes through the point $(5, 3)$. Find the coordinates of $A$.
Question 97:
Prove that the product of the lengths of the perpendiculars drawn from the points $(\sqrt{a^{2}-b^{2}},0)$ and $(-\sqrt{a^{2}-b^{2}},0)$; to the line $\frac{x}{a} \cos \theta+\frac{y}{b} \sin \theta=1$ is $b^2$.
Question 98:
A person standing at the junction (crossing) of two straight paths represented by the equations $2x-3y+4=0$ and $3x+4y-5=0$ wants to reach the path whose equation is $6x-7y+8=0$ in the least time. Find equation of the path that he should follow.