CBSE - Class 11 Mathematics Straight Lines Worksheet
1.
Find angles between the lines $\sqrt{3}x + y = 1$ and $x + \sqrt{3}y = 1$.
2.
The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.
3.
In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line $x + y = 4$?
4.
Find equation of the line perpendicular to the line $x – 7y + 5 = 0$ and having x intercept 3.
5.
Find the image of the point (3, 8) with respect to the line $x +3y = 7$ assuming the line to be a plane mirror.
6.
Find the distance of the line $4x + 7y + 5 = 0$ from the point (1, 2) along the line $2x – y = 0$.
7.
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
8.
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.
9.
Find perpendicular distance from the origin to the line joining the points (cos$\theta$, sin$\theta$) and (cos$\phi$, sin$\phi$).
10.
Passing through the points (–1, 1) and (2, – 4).
11.
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 $3x + y = 0$.
12.
The vertices of $\Delta$ PQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.
13.
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.
14.
Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
15.
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.
16.
Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts. (iii) $y = 0$.
17.
Find the angle between the x-axis and the line joining the points (3,–1) and (4,–2).
18.
Find the distance between P ($x_1$, $y_1$) and Q ($x_2$, $y_2$) when : (ii) PQ is parallel to the x-axis.
19.
Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
20.
Find the points on the x-axis, whose distances from the line $\frac{x}{3} + \frac{y}{4} = 1$ are 4 units.
