Question Related to Slope of a Line
Class XI » [Module : 10.1]
Que1. Find the
slope of a line whose inclination is: (i) 30° (ii) 120°
Que2. Find the
slope of a line passing through following points:
(i) (-2, 3) and
(4, 5) (ii)
(3,-2) and (3,4) (iii) (4,-2) and (6,-2) (iv)
Que3. Find the
slope of a line which bisects the first quadrant angle.
Que4. Find the
slope of the line, which makes an angle of 30° with the positive direction of
y-axis measured anticlockwise.
Que5. Determine
x so that 2 is the slope of the line through the point (2.5) and (x, 3)
Que6. What is
the slope of line passing through origin and the mid point of the line segment
joining the point (2,-5), (3, 2)?
Que7. Find the
angle between the lines joining the points (6, 3), (1, 1) and(–3,5), (2, 6).
Que8. Find the
angle between the y-axis and the line joining the points (3,-1) and (4,-2).
Que9. Using
slopes, show that the points A(4, 8), B(5, 12), C(9, 28) are collinear
Que10. Find the
value of x for which the points (x,-1), (2, 1) and (4, 5) are collinear
Que11. Show that
the line joining (2,-3) and (–5, 1) is parallel to the line joining (7,-1) and
(0, 3).
Que12. Show that
the line Joining (2,-5) and (-2, 5) is perpendicular to the line joining (6, 3)
and (1, 1).
Que13. check the
line joining (2,-5) and (-2, 5) is parallel to the line joining (6, 3) and (1,
1).
Que14. The straight
line joining the points (-2, 5) and (-4, 3) is perpendicular to the line
joining the points (K, 0) and (2, 3K); find K.
Que15. If three
points A(h, 0), P(a, b) and B(0, K) lie on a line, show that
Que16. The slope
of a line is double of the slope of another line. If tangent of the angle
between them is 1/3, find the slopes of the other line.
Que17. Prove
that the four points with co-ordinates (-4, 0), (6, 4), (5.0) and (0,-2) are
the vertices of a trapezium
Que18. Without
using distance formula, show that points (-2, -1), (4,0), (3, 3) and (- 3, 2)
are the vertices of a parallelogram.
Que19. Using
slopes, prove that the points (-4, -1), (-2,-4), (4, 0) and (2, 3), taken in
order, are the verdices of a rectangle.
Que20. A
quadrilateral has vertices (4, 1), (1, 7), (-6, 0) and (–1, –9) Show that the
mid points of the sides of this quadrilteral form a parallelogram.
Question
Related to Slope of a Line
Class XI » [Module : 10.2]
Que1. Find the slope of a line whose inclination is
(i) 30° (ii) 150°
Que2. Find the inclination of the line having slope:
(i) –1 (ii)√3 (iii) 1
Que3. Find the slope of a line passing through the
following points:
(i) (4.-6) and (-2,-5) (ii) (3,-5) and (1, 2) (iii) (a, b) and (b, a) (iv) (0,-4) and (-6, 2)
Que4. If a line is equally inclined to the axes, show
that its slope is 1.
Que5. Determine x so that the inclination of the line
containing the points (x,–3) and (2,5) is 135.
Que6. Slope of a line joining the points (7, 3) and
(K. 2) is-4. Find the value of K.
Que7. What is the value of y so that the line through
(3, y) and (2, 7) is parallel to the line through (–1, 4) and (0,6)?
Que8. Find the angle between the x-axis and the line
joining the points (3,–1) and (4,–2).
Que9. Show that the line joining the points (2,-3) and
(-5, 1) is parallel to the line joining the points (7,-1) and (0, 3).
Que10. Show that the line joining the points (2,-5)
and (-2, 5) is perpendicular to the line joining (6, 3) and (1,1).
Que11. Find the angle between the lines joining the
points (-1, 2), (3,-5) and (-2, 3), (5, 0).
Que12. If the 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.
Que13. Without using pythagoras theorem, show that the
points (1, 2), (4, 5) and (6, 3) represent the vertices of a right triangle.
Que14. Using slopes, show that the points P (6.-1).
Q(5, 0) and R(2, 3) are collinear,
Que15. Find the value of x for which the points
(x,-1), (2, 1) and (4, 5) are collinear.
Que16. Using slopes, show that the vertices (-2,-1),
(4, 0), (3, 3) and (-3, 2) are the vertices of a parallegoram.
Que17. Using slope, show that P(2,-2), Q(8, 4), R(5, 7)
and S(-1, 1) are the vertices of a rectangle.
Que18. A quadrilateral has the vertices at the points
(-4,2), (2, 6), (8, 5) and (9,-7). Show that the mid points of the sides of
this quadrilateral are vertices of a parallelogram.
Que19. The slope of a line is three times the slope of
another line. If the tangent of the angle between them is 1/2, find the slopes
of the lines.
Que20. If the angle between two lines is
Que21. Find the acute angle between the y-axis and the
line joining the points (4, 3√3) and (3, 2√3).
Questions
Related to Different form of a Line
Class XI »
[Module : 10.3]
1. Find the equation of the following lines:
(i) parallel to X-axis and 2 units above it.
(ii) parallel to X-axis and 3 units below it.
(iii) parallel to Y-axis and 6 units left of it.
(iv) parallel to Y-axis and 4 units right of it.
2. Find the equation of a line which passes through
the point (1,-1) and parallel to
(i) X-axis (ii) Y-axis
3. Find the equation of line passing through the point
(2, 6) and perpendicular to
(i)X-axis (ii) Y-axis
4. Find the equation of a line passing through the
point (1,-2) and whose slope is 4.
5. Find the equation of a line passing through the
point (-2, 0) and makes an angle of
6. Find the equation of a line passing through the
point (0, -2) and makes an angle of 75o from the positive direction
of X-axis.
7. (i) Find the equation of a line passing through
origin and makes an angle of 60o from the positive direction
of X-axis.
(ii)Find the
equation of a line for which tan 0-2 and the length of intercept on X-axis is 3
units.
8. (i) Find the equation of line passing through (2,
2) and makes an angle of 135o from positive direction of X-axis.
(ii) Find the
equation of a line passing through the point (2,1) and makes an angle
9. Find the equation of the line passing through the
following points:
(i) (1,
2) and (4, 7)
(ii) origin and (1, 4)
(iii) (-3,
1) and (0, 3) (iv)
(-2,-3) and (1, 2)
10. (i) Find the equation of a line passing through
the points (a, b) and (ab, b²).
(ii) The
vertices of a triangleABC are A(2,5), B(3,2) and C(5,6). Find the equation of
the bisector of
11. If the point (p. q) lies on the line joining the
points (-4, 5) and (-5, 7), then show that 2p+q+3=0.
12. Find the equation of the medians of
13. The vertices of
14. Find the equation of the perpendicular bisector of
the line segment joining the points (1, 0) and (3, 5).
15. Show that the points (0, 3), (-2,-2) and (2, 8)
are collinear. Also find the equation of line through these points.
16. Find the equation of a line whose:
(i) slope = –1
and Y-intercept = 3.
(ii) slope =
(iii) slope =
17. Find the equation of a line which intersects
Y-axis at a distance of 4 units above origin and makes an angle of 45° from
positive direction of X-axis.
18. Find the Y-intercept of the line 2y=4x–3.
19 . Find the equation of a line which intersects
X-axis at a distance of 2 units on right of origin and makes an angle of 30°
from positive direction of X-axis.
20. Find the equation of lines whose X and
Y-intercepts are as follows:
(i) 2 and 3 (iii) 3 and -5
(ii)-2 and -5 (iv) 4 and -2
21. Find the intercepts cuts on X-axis and Y-axis from
the following lines:
(1) 3x + 4y = 12 (ii) 2x-5y=8 (iii) x+2y+3=0 (iv) 2x-y+3=0
22. Find the equation of a line which passes through
the point (1, 3) and makes equal intercepts on X and Y-axis.
23. Find the equation of a line which passes through
(-3, 2) and makes intercepts equal in magnitude but opposite in sign on X and
Y-axis.
24. Find the equation of a line passes through (3, 4)
and the ratio of its intercepts on X and Y-axis is 3:2.
25. Find the equation of a line passing through the
point (2, 2) and sum of whose intercepts on X and Y-axis is 9.
26. (i) Find the intercepts made by line 5x-2y= 10 on
both axes. Also find the length of segment between the axes made by lines.
(ii) Find the equation of a line whose X and Y
intercepts are respectively 3 and 4 times of the intercepts of the line 2x +
3y=6.
27. (i) Find the equation of a line, in which the
mid-point of the line segment between the axes is (-3, 2).
(ii) Find
the area of triangle formed by the line 4x + 3y = 24 and the co-ordinate axes.
28. Find the equation of a line whose segment between the axes is divided in the ratio 2:3 by the point (h, k).
29. Find the equation
of a line which is at a perpendicular distance of √2 units from origin and the
perpendicular from origin to this line makes an angle of 135" from
positive direction of X-axis.
30. Find the equation of a line which is at a distance
of 2 units from origin and the perpendicular from origin to this line makes an
angle tan-112 from positive direction of X-axis.
31. Find the equation of a line which is at a distance
of 4 units from origin and the slope of perpendicular from origin to this line
is √3
32. Find the equation of a line which makes a triangle
of area 96√3 square units from co-ordinate axes and the perpendicular drawn
from origin to this line makes an angle 60° from X-axis.
