हिंदी

Find the Slope of the Lines Which Make the Following Angle with the Positive Direction of X-axis: 2 π 3

Advertisements
Advertisements

प्रश्न

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

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

संक्षेप में उत्तर
Advertisements

उत्तर

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

\[\therefore \text { Slope of the line } = m = \tan\theta\]

\[ \Rightarrow \text { Slope of the line }= \tan\left( \frac{2\pi}{3} \right) = - \tan\left( \frac{\pi}{3} \right) = - \sqrt{3}\]

Hence, the slope of the line is \[- \sqrt{3}\].

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: The straight lines - Exercise 23.1 [पृष्ठ १२]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 23 The straight lines
Exercise 23.1 | Q 1.2 | पृष्ठ १२

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).


Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line x –2y = 3.


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

\[- \frac{\pi}{4}\]


Find the slope of a line (i) which bisects the first quadrant angle (ii) which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.


Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).


Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .


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 positive ?


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).


Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.


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


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. 


Find the equation of a straight line with slope 2 and y-intercept 3 .


Find the equation of a straight line  with slope − 1/3 and y-intercept − 4.


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 equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.


If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.


Find the angles between the following pair of straight lines:

3x + 4y − 7 = 0 and 4x − 3y + 5 = 0


Find the acute angle between the lines 2x − y + 3 = 0 and x + y + 2 = 0.


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


Show that the tangent of an angle between the lines \[\frac{x}{a} + \frac{y}{b} = 1 \text { and } \frac{x}{a} - \frac{y}{b} = 1\text {  is } \frac{2ab}{a^2 - b^2}\].


The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is 


The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is


The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is  


Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.


The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are ______.


The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.


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).


If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.


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.


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


The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.


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). The co-ordinates of the point A is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×