Advertisements
Advertisements
Question
Find the acute angle between the X-axis and the line joining points A(3, −1) and B(4, −2).
Advertisements
Solution
Given: A(3, −1) and B(4, −2)
∴ Slope of line AB = m = `(-2 - ( - 1))/(4 - 3)`
= `(-2 + 1)/1`
= − 1
Let θ be the acute angle between the X-axis and the line AB.
∴ m = tan θ, which is positive
∴ tan θ = |− 1| = 1 = tan 45°
∴ θ = 45°
APPEARS IN
RELATED QUESTIONS
Find the slope of the following line which passes through the points:
C(−2, 3), D(5, 7)
Find the slope of the following line which passes through the points:
E(2, 3), F(2, −1)
Find the slope of the following line which passes through the points:
G(7, 1), H(−3, 1)
If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1
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
Select the correct option from the given alternatives:
The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is
Select the correct option from the given alternatives:
If kx + 2y − 1 = 0 and 6x − 4y + 2 = 0 are identical lines, then determine k
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 points A(1, 3), B(4, 1), C(3, k) are collinear
Find the equation of the lines passing through the point (1,1) with slope 3
Find the equation of the lines passing through the point (1, 1) and the perpendicular from the origin makes an angle 60° with x-axis
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
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 value of C for 98.6°F
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 value of F for 38°C
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
Population of a city in the years 2005 and 2010 are 1,35,000 and 1,45,000 respectively. Find the approximate population in the year 2015. (assuming that the growth of population is constant)
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using a straight line
A 150 m long train is moving with constant velocity of 12.5 m/s. Find time taken to cross a pole
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.
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 |
How long will the spring be when 6 kilograms of weight on it?
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
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 coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) internally in the ratio 2 : 3.
