English

What Can Be Said Regarding a Line If Its Slope is Zero ?

Advertisements
Advertisements

Question

What can be said regarding a line if its slope is  zero ?

One Line Answer
Advertisements

Solution

 If the slope of a line is zero, then the line is either the x-axis itself or it is parallel to the x-axis.

shaalaa.com
  Is there an error in this question or solution?
Chapter 23: The straight lines - Exercise 23.1 [Page 13]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 23 The straight lines
Exercise 23.1 | Q 7.1 | Page 13

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

The base of an equilateral triangle with side 2a lies along they y-axis such that the mid point of the base is at the origin. Find vertices of the triangle.


If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`


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


Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is 

  1. Parallel to the x-axis,
  2. Parallel to the y-axis,
  3. Passing through the origin.

Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.


Find the slope of the lines which make the following angle with the positive direction of x-axis:

\[\frac{2\pi}{3}\]


State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)


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)?


What can be said regarding a line if its slope is negative?


Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).


Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).


Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.


The slope of a line is double of the slope of another line. If tangents of the angle between them is \[\frac{1}{3}\],find the slopes of the other line.


By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.


A quadrilateral has vertices (4, 1), (1, 7), (−6, 0) and (−1, −9). Show that the mid-points of the sides of this quadrilateral form a parallelogram.


Find the equations of the bisectors of the angles between the coordinate axes.


Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.


Find the equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.


Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).


Prove that the points (2, −1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.


If θ is the angle which the straight line joining the points (x1, y1) and (x2, y2) subtends at the origin, prove that  \[\tan \theta = \frac{x_2 y_1 - x_1 y_2}{x_1 x_2 + y_1 y_2}\text { and } \cos \theta = \frac{x_1 x_2 + y_1 y_2}{\sqrt{{x_1}^2 + {y_1}^2}\sqrt{{x_2}^2 + {y_2}^2}}\].


Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.


Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.


Find k, if the slope of one of the lines given by kx2 + 8xy + y2 = 0 exceeds the slope of the other by 6.


If the slopes of the lines given by the equation ax2 + 2hxy + by2 = 0 are in the ratio 5 : 3, then the ratio h2 : ab = ______.


A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.


Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1).


A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.


P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.


Slope of a line which cuts off intercepts of equal lengths on the axes is ______.


The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.


Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.


The point (4, 1) undergoes the following two successive transformations: 
(i) Reflection about the line y = x
(ii) Translation through a distance 2 units along the positive x-axis Then the final coordinates of the point are ______.


Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.


Line joining the points (3, – 4) and (– 2, 6) is perpendicular to the line joining the points (–3, 6) and (9, –18).


Column C1 Column C2
(a) The coordinates of the points
P and Q on the line x + 5y = 13 which
are at a distance of 2 units from the
line 12x – 5y + 26 = 0 are
(i) (3, 1), (–7, 11)
(b) The coordinates of the point on
the line x + y = 4, which are at a  unit
distance from the line 4x + 3y – 10 = 0 are
(ii) `(- 1/3, 11/3), (4/3, 7/3)`
(c) The coordinates of the point on the line
joining A (–2, 5) and B (3, 1) such that
AP = PQ = QB are
(iii) `(1, 12/5), (-3, 16/5)`

The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and

Column C1 Column C2
(a) Through the point (2, 1) is (i) 2x – y = 4
(b) Perpendicular to the line (ii) x + y – 5
= 0 x + 2y + 1 = 0 is
(ii) x + y – 5 = 0
(c) Parallel to the line (iii) x – y –1 = 0
3x – 4y + 5 = 0 is
(iii) x – y –1 = 0
(d) Equally inclined to the axes is (iv) 3x – 4y – 1 = 0

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×