मराठी

Find the Slope of the Lines Which Make the Following Angle with the Positive Direction of X-axis: 3 π 4 - Mathematics

Advertisements
Advertisements

प्रश्न

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

\[\frac{3\pi}{4}\]

थोडक्यात उत्तर
Advertisements

उत्तर

\[\theta = \frac{3\pi}{4}\]

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

\[ \Rightarrow \text { Slope of the line } = \tan\left( \frac{3\pi}{4} \right) = - \tan\left( \frac{\pi}{4} \right) = - 1\]

Hence, the slope of the line is \[- 1\].

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

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 23 The straight lines
Exercise 23.1 | Q 1.3 | पृष्ठ १२

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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.


Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).


Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.


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


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


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

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


Find the slope of a line passing through the following point:

 (−3, 2) and (1, 4)


Find the slope of a line passing through the following point:

\[(a t_1^2 , 2 a t_1 ) \text { and } (a t_2^2 , 2 a t_2 )\]


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

Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)


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


If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: \[\frac{a}{h} + \frac{b}{k} = 1\].


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.


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.


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


Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.


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.


Find the angles between the following pair of straight lines:

3x + y + 12 = 0 and x + 2y − 1 = 0


Find the angles between the following pair of straight lines:

3x − y + 5 = 0 and x − 3y + 1 = 0


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


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 \[\left( \frac{a}{b} \right)\].


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


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


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 ______.


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


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 ______.


Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).


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.


If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.


The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.


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).


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×