Advertisements
Advertisements
प्रश्न
Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).
Advertisements
उत्तर
The slope of the line joining the points (3, –1) and (4, –2) is:
m = `(-2-(-1))/(4 - 3)`
`= -2 + 1`
= –1
Now, the inclination (θ) of the line joining the points (3, –1) and (4, –2) is given by
tan θ = –1
⇒ θ = (90° + 45°) = 135°
Thus, the angle between the x-axis and the line joining the points (3, –1) and (4, –2) is 135°.
Angle between the line and the x-axis 45∘
APPEARS IN
संबंधित प्रश्न
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
If three point (h, 0), (a, b) and (0, k) lie on a line, show that `q/h + b/k = 1`
Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
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:
(3, −5), and (1, 2)
What can be said regarding a line if its slope is positive ?
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 angle between X-axis and the line joining the points (3, −1) and (4, −2).
By using the concept of slope, show that the 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 −2 and intersecting the x-axis at a distance of 3 units to the left of origin.
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 equations of the straight lines which cut off an intercept 5 from the y-axis and are equally inclined to the axes.
The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.
Find the angles between the following pair of straight lines:
3x + y + 12 = 0 and x + 2y − 1 = 0
Write the coordinates of the image of the point (3, 8) in the line x + 3y − 7 = 0.
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
If x + y = k is normal to y2 = 12x, then k is ______.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlock wise direction through an angle of 15°. Find the equation of the line in new position.
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
Find the angle between the lines y = `(2 - sqrt(3)) (x + 5)` and y = `(2 + sqrt(3))(x - 7)`
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).
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.
P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.
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 equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.
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 (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.
The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.
