CBSE - Class 11 Mathematics Straight Lines Worksheet
1.
Find equation of the line perpendicular to the line $x – 7y + 5 = 0$ and having x intercept 3.
2.
Find the values of $k$ for which the line $(k–3) x – (4 – k^2) y + k^2 –7k + 6 = 0$ is (a) Parallel to the x-axis,
3.
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.
4.
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.
5.
Find equation of the line parallel to the line $3x - 4y + 2 = 0$ and passing through the point (–2, 3).
6.
Point R ($h$, $k$) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.
7.
Find the values of $k$ for which the line $(k–3) x – (4 – k^2) y + k^2 –7k + 6 = 0$ is (b) Parallel to the y-axis,
8.
Reduce the following equations into intercept form and find their intercepts on the axes. (ii) $4x – 3y = 6$
9.
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.
10.
Find the distance between P ($x_1$, $y_1$) and Q ($x_2$, $y_2$) when : (ii) PQ is parallel to the x-axis.
11.
Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
12.
Find the area of the triangle formed by the lines $y – x = 0$, $x + y = 0$ and $x – k = 0$.
13.
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).
14.
Find the distance of the point (–1, 1) from the line $12(x + 6) = 5(y – 2)$.
15.
Find the value of $p$ so that the three lines $3x + y – 2 = 0$, $px + 2 y – 3 = 0$ and $2x – y – 3 = 0$ may intersect at one point.
16.
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.
17.
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.
18.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).
19.
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
20.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
