मराठी

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

Advertisements
Advertisements

प्रश्न

Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]

थोडक्यात उत्तर
Advertisements

उत्तर

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

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

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

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 23: The straight lines - Exercise 23.1 [पृष्ठ १२]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 23 The straight lines
Exercise 23.1 | Q 1.4 | पृष्ठ १२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).


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


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

Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).


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


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, −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.


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


Without using the distance formula, show that points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.


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


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 angles between the following pair of straight lines:

x − 4y = 3 and 6x − y = 11


Find the angles between the following pair of straight lines:

(m2 − mn) y = (mn + n2) x + n3 and (mn + m2) y = (mn − n2) x + m3.


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


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.


Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.


Prove that the straight lines (a + b) x + (a − b ) y = 2ab, (a − b) x + (a + b) y = 2ab and x + y = 0 form an isosceles triangle whose vertical angle is 2 tan−1 \[\left( \frac{a}{b} \right)\].


If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.


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 equation of a line passing through the point (7, - 4) and perpendicular to the line passing through the points (2, 3) and (1 , - 2 ) is ______.


Point of the curve y2 = 3(x – 2) at which the normal is parallel to the line 2y + 4x + 5 = 0 is ______.


The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.


If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.


The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.


The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is ______.


Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.


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


One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.


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


The points A(– 2, 1), B(0, 5), C(– 1, 2) are collinear.


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 ______.


If the line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through an angle of 15°, then the equation of the line in new position is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×