English

Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise - Mathematics and Statistics

Advertisements
Advertisements

Question

Find the slope of the line which makes angle of 45° with the positive direction of the Y-axis measured anticlockwise

Sum
Advertisements

Solution


Since the line makes an angle of 45° with the positive direction of the Y-axis in the anticlockwise direction,

Inclination of the line (θ) = (90° + 45°)

∴ Slope of the line = tan(90° + 45°)

= −cot 45°

= −1

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Straight Line - Exercise 5.2 [Page 109]

RELATED QUESTIONS

Find the slope of the following line which passes through the points:

A(2, −1), B(4, 3)


If the X and Y-intercepts of lines L are 2 and 3 respectively then find the slope of line L.


Find the slope of the line whose inclination is 30°


A line makes intercepts 3 and 3 on the co-ordinate axes. Find the inclination of the line.


Find the value of k for which points P(k, −1), Q(2, 1) and R(4, 5) are collinear.


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


Select the correct option from the given alternatives:

A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y−interecpt is


Answer the following question:

Find the value of k if the slope of the line passing through the points P(3, 4), Q(5, k) is 9


Answer the following question:

Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)


Find the equation of the lines passing through the point (1, 1) with y-intercept (– 4)


If P(r, c) is midpoint of a line segment between the axes then show that `x/"r" + y/"c"` = 2


If p is length of perpendicular from origin to the line whose intercepts on the axes are a and b, then show that `1/("p"^3) = 1/("a"^2) + 1/("b"^2)`


The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F. Find the linear relationship between C and F


An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance between the place and the target


An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance covered by it in 15 seconds


An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find time taken to hit the target


Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12


Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using any other method


A straight line is passing through the point A(1, 2) with slope `5/12`. Find points on the line which are 13 units away from A


A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

Weight (kg) 2 4 5 8
Length (cm) 3 4 4.5 6

Draw a graph showing the results.


In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the heights at which the escalator changes its direction


Choose the correct alternative:
Straight line joining the points (2, 3) and (−1, 4) passes through the point (α, β) if


Choose the correct alternative:
Equation of the straight line perpendicular to the line x − y + 5 = 0, through the point of intersection the y-axis and the given line


Choose the correct alternative:
The line (p + 2q)x + (p − 3q)y = p − q for different values of p and q passes through the point


If one of the lines given by kx2 + 2xy – 3y2 = 0 is perpendicular to the line 3x + 5y+ 1 = 0, then the value of k is ______.


A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate, axes will lie only in ______.


The locus of the point of intersection of the lines xcosα + ysinα = α and xsinα – ycosα = b(where α is a variable) is ______.


The number of possible tangents which can be drawn to the curve 4x2 – 9y2 = 36, which are perpendicular to the straight line 5x + 2y – 10 = 0 is ______.


The coordinates of vertices of base BC of an isosceles triangle ABC are given by B(1, 3) and C(–2, 7) which of the following points can be the possible coordinates of the vertex A?


Find the transformed equation of the straight line 2x – 3y + 5 = 0, when the origin is shifted to the point (3, –1) after translation of axes.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×