CBSE - Class 11 Mathematics Straight Lines Worksheet
1.
Find the image of the point (3, 8) with respect to the line $x +3y = 7$ assuming the line to be a plane mirror.
2.
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.
3.
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,
4.
Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts. (i) $x + 7y = 0$
5.
Find the distance of the point (–1, 1) from the line $12(x + 6) = 5(y – 2)$.
6.
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 $\frac{1}{p^2} = \frac{1}{a^2} + \frac{1}{b^2}$.
7.
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 $b^2$.
8.
Reduce the following equations into intercept form and find their intercepts on the axes. (iii) $3y + 2 = 0$.
9.
If the lines $y = 3x +1$ and $2y = x + 3$ are equally inclined to the line $y = mx + 4$, find the value of $m$.
10.
Reduce the following equations into slope - intercept form and find their slopes and the y - intercepts. (ii) $6x + 3y – 5 = 0$
11.
Find the distance of the line $4x + 7y + 5 = 0$ from the point (1, 2) along the line $2x – y = 0$.
12.
Prove that the line through the point ($x_1$, $y_1$) and parallel to the line $Ax + By + C = 0$ is $A (x –x_1) + B (y – y_1) = 0$.
13.
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,
14.
Find the distance between parallel lines (i) $15x + 8y – 34 = 0$ and $15x + 8y + 31 = 0$
15.
Intersecting the x-axis at a distance of 3 units to the left of origin with slope –2.
16.
Find the distance between P ($x_1$, $y_1$) and Q ($x_2$, $y_2$) when : (i) PQ is parallel to the y-axis
17.
The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.
18.
The line through the points ($h$, 3) and (4, 1) intersects the line $7x - 9y - 19 = 0$ at right angle. Find the value of $h$.
19.
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.
20.
Find the distance between parallel lines (ii) $l (x + y) + p = 0$ and $l (x + y) – r = 0$.
