Advertisements
Advertisements
Question
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.
Advertisements
Solution
The slope of the line AB is `(1 - 0)/(3 - 2)` = 1 or tan 45° (Why?)
After rotation of the line through 15°
The slope of the line AC in new position is tan 60° = `sqrt(3)`
Therefore, the equation of the new line AC is
y – 0 = `sqrt(3) (x - 2)`
or `y - sqrt(3)x + 2sqrt(3)` = 0
APPEARS IN
RELATED QUESTIONS
Find the value of x for which the points (x, –1), (2, 1) and (4, 5) are collinear.
Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).
Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is
- Parallel to the x-axis,
- Parallel to the y-axis,
- Passing through the origin.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{3\pi}{4}\]
Find the slope of the lines which make the following angle with the positive direction of x-axis: \[\frac{\pi}{3}\]
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)
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.
Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).
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 coordinates of the orthocentre of the triangle whose vertices are (−1, 3), (2, −1) and (0, 0).
Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
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.
If θ is the angle which the straight line joining the points (x1, y1) and (x2, y2) subtends at the origin, prove that \[\tan \theta = \frac{x_2 y_1 - x_1 y_2}{x_1 x_2 + y_1 y_2}\text { and } \cos \theta = \frac{x_1 x_2 + y_1 y_2}{\sqrt{{x_1}^2 + {y_1}^2}\sqrt{{x_2}^2 + {y_2}^2}}\].
Show that the line a2x + ay + 1 = 0 is perpendicular to the line x − ay = 1 for all non-zero real values of a.
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 acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
Find k, if the slope of one of the lines given by kx2 + 8xy + y2 = 0 exceeds the slope of the other by 6.
If m1 and m2 are slopes of lines represented by 6x2 - 5xy + y2 = 0, then (m1)3 + (m2)3 = ?
If the slopes of the lines given by the equation ax2 + 2hxy + by2 = 0 are in the ratio 5 : 3, then the ratio h2 : ab = ______.
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 ______.
Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
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).
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.
Slope of a line which cuts off intercepts of equal lengths on the axes 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 ______.
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x – 2y = 3 are ______.
The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and
| Column C1 | Column C2 |
| (a) Through the point (2, 1) is | (i) 2x – y = 4 |
| (b) Perpendicular to the line (ii) x + y – 5 = 0 x + 2y + 1 = 0 is |
(ii) x + y – 5 = 0 |
| (c) Parallel to the line (iii) x – y –1 = 0 3x – 4y + 5 = 0 is |
(iii) x – y –1 = 0 |
| (d) Equally inclined to the axes is | (iv) 3x – 4y – 1 = 0 |
The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, 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 ______.
