Q. 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.

Q. Find the value of $x$ for which the points $(x,-1),(2,1)$ and $(4,5)$ are collinear.

Q. If three points $(h,0),(a,b)$ and $(0,k)$ lie on a line, show that $\frac{a}{h}+\frac{b}{k}=1.$

Q. 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.

Q. Find a point on the $x$-axis, which is equidistant from the points $(7,6)$ and $(3,4)$.

Q. Find the slope of the line, which makes an angle of ${30}^o$ with the positive direction of $y$-axis measured anticlockwise.

Q. Without using the Pythagoras theorem, show that the points $(4,4),(3,5)$ and $(1,1)$ are the vertices of a right angled triangle

Q. Draw a quadrilateral in the Cartesian plane, whose vertices are $(-4,5),(0,7),(5,-5)$ and $(-4,-2)$. Also, find its area.

Q. Consider the following population and year graph, find the slope of the line $AB$ and using it, find what will be the population in the year $2010$?

Q. 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 $B(8,0).$

Q. Without using distance formula, show that points $(-2,-1),(4,0),(3,3)$ and $(-3,2)$ are the vertices of a parallelogram

Q. Find the angle between the $x$-axis and the line joining the points $(3,-1)$ and $(4,-2)$.

Q. Find the distance between $P$ $(x_1,y_1)$and $Q$ $(x_2,y_2)$ when

Q. A line passes through $(x_1,y_1)$ and $(h,k)$. If slope of the line is $m$, show that $k-y_1=m(h-x_1)$

Q. Write the equations for the $x$-and $y$-axes.

Q. Find the equation of the line passing through $(2,2\sqrt{3})$ and inclined with the $x$-axis at an angle of 75${}^{\circ }$

Q. Find equation of the line passing through $(0,0)$ with slope $m$.

Q. Find equation of the line passing through the point $(-4,3)$ with slope $\frac{1}{2}$

Q. Find the equation of the line intersecting the $x$-axis at a distance of $3$ units to the left of origin with slope $-2.$

Q. 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.